You said you weren't that familiar with LoK ships, so I thought I'll give you a little bit of information about Lin-ships! (and also my opinion) :)
This ship is pretty obvious, as the two were together in canon. It's not known when the two got together, but they broke up sometime between 153-159 AG. The two have a lot in common, the pressure to meet their parents' expectations and they are both also very focused and serious, but the biggest difference is that Lin doesn't want children and Tenzin has a whole culture on his shoulders. Many ship it within canon, but also some in AU's where they get together again or do not break up at all. Very solid ship, especially since you often write about kid and teenage Lin, into which the ship can be integrated very easily.
This ship is quite popular desptie not being canon. The two benefit from the saying that opposites attract each other and can therefore complement one another very well. Many ship it mainly after the Linzin breakup, but some also in AU's where they get together earlier or have been attracted to each other for a long time. Kya is a lesbian in canon and since Lin's sexuality is unknown, she's mostly written as bisexual or gay.
This is a rather small ship, compared to the previous two. As with Kyalin, it's the same case here that opposites attract each other, but with Bumi more in a humorous way. The ship is definitely mostly written at an older age, due to the greater age difference.
Probably one of the smallest ships on the list, but it's getting more and more attention lately. There's not much to say about it personality wise, as Izumi hardly had any screen time, but many interpret her as rather serious and no nonsense, which is why the ship has some similarities to Linzin, in my opinion.
Personally, I don't ship it, because the age difference is too big for me, which is why it's definitely a ship for after the series. The two have very similar personalities and in some cases similar experiences, through which they can establish a connection.
This is also a rather small ship, which is mostly written at an advanced age. It's often the case that they fall in love, while one is still with Tenzin. I'm not sure if they'll be a good match based on their personality, but it's definitely an amusing ship.
7. Bonuses (without explanation)
Linorra (Lin & Korra), Kyalinzumi (Lin, Kya & Izumi), Pemlinzin (Lin, Tenzin & Pema)
I really hope this helps and that it wasn't to much. I Hope you have a great day. :3
Hi Anon, thank you for the ask! And YAY a list! :D You've done the hard work for me, and I'm forever grateful hehe.
Now that I'm seeing this list, most of these are ships I've seen roaming around the dash, although I don't have many strictly LOK conversations with people at the moment.
The Lin ships with the cloudbabies are what probably make the most sense to me, but all of them seem cool! I will say that I don't often have the original cloudbabies in my stories, only because I don't often write Kataang, but I can see the opportunity for some interesting coming of age stories for the next gen if I were to stick with canon.
Actually, how funny would it be if Lin dated all the cloudbabies? LOL. Probably unlikely, but a funny thought nonetheless ;)
I kind of like the idea of Linzin when they're teens, and then if canon were to occur and Tenzin was with Pema, it would be interesting to see the opposites attract dynamic with Bumi. They can relate a bit to being the oldest sibling, having a big legacy/reputation, and (potentially) feeling like they were disappointing their parents growing up. Also, I feel like both Bumi II and Lin could use some hugs lmao.
Fun! Thank you for this list of ships, Anon. It definitely helps me out a ton, and I can't believe you took the time to compile this for me :') You Nonnies are so nice to me, it makes my heart swoon.
Thank you again for this ask and the list of ships, and I hope you have a great day!
Send me asks about ATLA, or anything, really! :D