Things I’m happy with:

3 of each common appears to be the right number for redundancy without enabling the decks that I don’t want to see with 5+ of the same card

2 of each uncommon gives enough that each archetype should have one floating around in the pool and possibly two

There were enough cards in the Dimir colors to build two similar decks without one being ridiculously overpowered

No mythics actually felt right so I’m actually just going to leave them out for now

Dream Fracture was a huge blowout

Favored Winds is a huge beating with the right support

Stronghold Discipline was surprisingly effective against my Azorius flyers/tokens deck

Academy Researchers was amazing in the Dimir deck

The Will of the Council cards were always fun to resolve even if they went against what you wanted

Things I’m not happy with:

Reya Dawnbringer came down far too late to be relevant which is not what I want to see out of rares

Stifle and Misdirection were both disappointing because of the number cards with a reduced

Magus of the Mirror is too slow to be interesting

Exploration sat in the sideboard because you have to be deep in blue for it to be relevant due to not having the card flow

Reflecting Pool doesn’t fix mana the way I would like for a rare

I'm pretty sure a lot of the reprint rares I'm just going to swap out. It seems like a lot of them were selected for making reprints more available rather than them being particularly relevant.  I want the rares to be things that break stalemates to avoid massive board stalls and can push things to a conclusion.

Reprint rares:

(Out) Reya Dawnbringer - too expensive and too slow, would be best as a reanimation target

(In) Rout - a good sweeper is what I want to see as a rare

(Out) Misdirection - not enough single target things to make it worth playing

(Out) Stifle - multiplayer is not conducive to the tempo plays Stifle is best with

(In) Ill-Gotten Gains - was very cool when it was played; lots of power but politically charged

(Out) Magus of the Mirror - really needs to be usable any time, the upkeep restriction makes it incredibly hard to use

(In) Heartless Hidetsugu - does a great job of putting people on a clock and can be very relevant for multiple archetypes

(On the fence) Sulfuric Vortex - not sure about this one yet, need to see someone play it effectively as several of the red decks are slower

(Out) Exploration - only good with a ton of blue cards to keep the lands flowing, would rather just have a more universally effective card

(In) Terastodon - great at dealing with the artifacts and enchantments that enable a lot of shenanigans and has plenty of political implications

(In) Wolfbriar Elemental - great bomb that can break the game open late or catch you up

(In) Basandra, Battle Seraph - very solid stall breaker and large evasive body

(In) Decimate - 4 for 1s are exactly the kind of removal needed most of the time

(In) Dimir Doppleganger - plays exceptionally well in the Dimir deck as a ever-changing threat depending on what they’ve played so far

(On the fence) Edric, Spymaster of Trest - the Simic deck really isn’t trying to go wide and it’s not a great political deck, but he might still make the cut depending on what I decide to do with the archetype

(In) Spiritmonger - Golgari desperately needs big beater to finish out the game after all the attrition and Spiritmonger is a nice balanced way to handle it

(On the fence) Altar of Dementia - In theory it’s cool because it’s a free sac outlet, but really none of the archetypes have a good way to take advantage of it

(On the fence) Deathrender - A moderate power and toughness boost with the potential for shenanigans

There's several archetypes that occasionally come up as options.  Rather than beat them all to death like I did the main ten color pairs, I'm just going to list them with a brief description and some of the important cards, as most of them are based on getting a particular rare or uncommon and shaping the draft around it.

Archetype 1: 5 color Worldknit

This deck, while obvious, is also the easiest to explain.  If you see a Worldknit early, you can easily just draft the best card each pick as long as it fits your curve.  We have yet to see a Worldknit before pack 2 in my group, and we've been drafting with 4 packs for testing purposes and because we enjoyed it much more than only 3 with 4 players.

Most important card(s): Worldknit

Archetype 2: Grixis Dethrone

Very similar to the Izzet dethrone deck, but with more removal.  Usually happens when someone opens Marchesa and wants to live the dream.  The main reason to push it is black removal makes it much easier to open up the way for your attackers.

Most important cards(s): Marchesa, the Black Rose; solid black removal

Archetype 3: Kindred Commons + Conspiracies

Every color has at least one or two vanilla or french vanilla creatures that won't be picked highly that are borderline playable.  The idea here is to draft all the conspiracies and figure out which color is open so you can grab 3-4 of a particular common, name it with your conspiracies, and get undercosted creatures to stomp face with or play multiple spells with the same name for a similar effect.

Most important card(s): Secret Summoning and Muzzio's Preparations for creatures, Double Stroke and Iterative Analysis for non creatures.

Archetype 4: Flamekin Pants (R/x Auras)

This deck is all about getting 1 or 2 Flaring Flame-kin and trying to turn them into a giant unbeatable monster.  I've drafted this once before after starting in Izzet and not seeing the dethrone cards coming around.  It's quite fun to play but the best auras are G/W.  This archetype is much more luck based than some of the others as it requires several uncommons to be really good, but it's great when you can pull it off.

This update has taken me forever to get back to, mostly because it took several drafts to get this monstrosity of an archetype to actually work.  In theory, you're supposed to be able to be able to just draft tons of creatures then dig to them and overwhelm people.  The problem is, without the conspiracies to back you up this archetype very rarely works.  You're also very vulnerable to anyone else going into green, because blue really doesn't have the big monsters to support this properly.  All that said, if no one's going after the green creatures you're fine.

Best uncommons for this archetype:

Air Servant - one of the best evasive beaters in the set

Jetting Glasskite - another evasive beater that's difficult to target

Lead the Stampede - restocking your hand to get more creatures is key to victory for this archetype

Pelakka Wurm - Simic is, more than anything else, the go big or go home color combo and most other decks won't be able to support this

Wood Sage - seeder uncommon designed to help you dig for answers

Best commons for this archetype:

Compulsive Research - you'll likely be digging for lands early and creatures late

Elvish Aberration - mana early, beater late

Howling Wolf - one of the value commons that you'll want; even though it feels really overcosted you'll need to draft it early to make sure you have enough

Screaming Seahawk - see Howling Wolf, only this one is much more playable with only 2

Shoreline Ranger - mana early, beater late that also flies

As you can see above, this archetype has some of the most boring commons and uncommons that you want to draft highly.  None of the new cards in Conspiracy were really intended for this archetype outside of the conspiracies themselves.  This archetype works fine if no one else drafts 2 or more of a particular creature and actually wants the conspiracies, but my group has long since discovered the power of free stuff and they always go highly regardless of the colors people are in.

Izzet does something very different in this set - it attacks, and often.  Normally Izzet decks do something more offbeat like focus on artifacts or it's a spell based archetype with supporting mechanics.  In Conspiracy, it's definitely an aggressive archetype looking for ways to keep attacking with its dethrone creatures until they're big enough to just outright win combat.  The deck is also very tempo-oriented.  You want to drop a bunch of dethrone creatures early and then back them up with removal and counterspells to keep getting in until you can start finishing people off.  Dethrone's an all-new mechanic for Conspiracy and it's definitely an interesting one to try and maximize. Between trying to maximize the amount of dethrone triggers you're getting as well as making sure you attacks are meaningful, you get a lot of interesting tension and decision making.  

Best uncommons for this archetype:

Marchesa's Infiltrator - decent dethrone guy that can keep your hand full while attacking

Marchesa's Smuggler - seeder uncommon that does everything the deck wants

Treasonous Ogre - gives you a way to accelerate a bit, but more importantly gives you a way to decrease your own life total to get dethrone triggers again

Uncontrollable Anger - combat trick that also plays well into what you want to do with your dethrone creatures anyway

Wind Dancer - makes your dethrone guys much harder to block

Best commons for this archetype:

Grenzo's Cutthroat - plays very well with the other combat tricks available due to first strike

Marchesa's Emissary - comes down a little later but a great target for enchantments or equipment due to hexproof

Orcish Cannonade - clears out an early blocker, helps keep your life lower than someone's, and cantrips

Traveler's Cloak - cantrips through your deck while making your dethrone guy unblockable against one or more opponents

Wrap in Flames - keeping up to 3 creatures from blocking almost guarantees a solid attack, perfect for later when you want to get multiple dethrone triggers in a single turn

Orzhov is the most controlling of the color pairs in Conspiracy.  I haven't played an archetype that was this controlling in a draft a significant amount previous to this format, but it definitely makes sense considering the differences in the multiplayer format.  At the same time, many of the cards are based around the new mechanic Will of the Council, which is very much a pick-your-poison type mechanic for multiplayer. You can always assume people will vote for whatever will benefit them the most (or help you the least, depending on the player) so it's a very political deck as well.

Best uncommons for this archetype:

Bite of the Black Rose - potential sweeper or discard, either should hopefully get you card advantage

Council Guardian - makes a great late game finisher as well as a great wall to make attacking miserable, especially if you can get more than one color out of it with multiple vote

Mortify - remove creatures as long as they don't have protection and destroy enchantments as necessary, arguably the best point removal in the set

Skeletal Scrying - great way to restock your hand after cleaning up the board with point removal

Unquestioned Authority - make your small creatures into finishers or very difficult to remove blockers

Best commons for this archetype:

Apex Hawks - blocks Spirit tokens early game or turns into a finisher late game

Brago's Representative - getting extra votes on your Will of the Council cards is very helpful, and he blocks very well

Custodi Squire - great source of recursion and a potential win condition that plays well with the other commons you want

Grudge Keeper - semi-unexciting body but can force through your Will of the Council votes so people can avoid damage 

Tyrant's Choice - board control or life loss, either works in your favor

Selesnya hits another tried and true archetype for Limited - make tokens and turn them sideways.  We saw this for Selesnya in both original Ravnica and Return.  The underlying theme is actually about making more creatures that your opponents can handle, and that is usually done one of two ways but preferably both.  You can either flood the board with enough creatures that you can get in for damage through their blockers, or you can make your creature more difficult to block profitably.  A good tokens deck does both of these things.  For multiplayer, you also need a way to get card advantage because your weenie tokens will almost certainly end up dying to your opponent's removal/blockers.  Fortunately, we have Parley in the set, which are also appealing for the archetype as the best ones make more tokens.

Best uncommons for this archetype:

Intangible Virtue - vigilance is one of the most useful multiplayer keywords, and boosting your tokens is fantastic

Predator's Howl - your tokens will die in combat; making extras is a great consolation prize

Selvala's Charge - makes board-relevant tokens and replaces itself

Squirrel Nest - 1/1 for 1 that doesn't cost you a card is exactly what this deck wants

Woodvine Elemental - nothing says play tokens like a repeatable overrun

Best commons for this archetype:

Copperhorn Scout - untapping your team is key to making your opponents look elsewhere for attacks

Doomed Traveler - beats early, chump blocks mid game to turn into a flyer

Echoing Courage - tokens of a particular type all have the same name

Rousting of Souls - huge part of what makes this deck work

Wrap in Vigor - saves your team from sweepers and lets you attack into messy board states

Gruul hits the standard notes for a RG draft archetype (at least since Scars of Mirrodin) - ramp into fatties.  The first time I heard the “Dinosaurs” name for the archetype was in Scars of Mirrodin.  It’s probably because Alpha Tyrranax and Molder Beast look very classical dinosaur-esque.  The key is having the acceleration available to make it possible to play these guys a few turns early and just run over your opponents before they can catch up with your mana advantage.

Best uncommons for this archetype:

Boldwyr Intimidator - huge guy that can make himself and your team unblockable with all your excess mana

Deathforge Shaman - sometimes it’s more expedient to just go right to the dome

Lead the Stampede - this should be at least a consistent 2 for 1, and could potentially be a lot bigger

Fires of Yavimaya - only thing better that early fatties is early fatties that attack a turn early so your opponents can’t plan for it 

Pelakka Wurm - huge guy that gives you a bonus coming in and going out

Best commons for this archetype:

Chartooth Cougar - make sure you hit your land drops early, firebreathing beater late

Charging Rhino - big guy that can’t be team blocked

Sakura-Tribe Elder - key piece of the deck for obvious reasons

Skitter of Lizards - hasty beats early, hasty dinosaur late

Sporecap Spider - does a great job of keeping almost everything from attacking profitably while you set up your dinosaurs