Bin cage: These are incredible since they're sooo versatile. If you decide you'd like to make a bin cage (using a storage bin with added ventilation) this will be the cheapest housing option. The smallest recommended size is a 110 qt sterilite bin, but any size larger in that brand or the largest IKEA SAMLA bin are also acceptable! If you have the space to do a larger enclosure, also look at 200 qt bins and xmas tree bin. Check out this video on how to ventilate since I am silly and cannot use my brain right now to explain it https://www.youtube.com/watch?v=cjuWsbPrF04

The main thing to avoid is bins with wheels underneath, the plastic over the wheels bumps up inside and makes for a great spot to chew and escape from!

Tank: Tanks are great for allowing for the most bedding possible, and functionally prevent any messes the ham could make. You'll want to look for a 40 gallon at least, if you have a petco near you they regularly (like 5-6 times a year) do a sale where they offer half off on all their tanks (its going on right now actually) so a 40 would be $60 currently. 55 gallon tanks are technically smaller, but they are very tall and allow for a LOT deeper bedding and more climbing enrichment, and 60 and 75 gallon tanks have the same floor space as each other, but the 75 is taller. If you decide on a tank you'll need to order the tank lid online for any size over a 40 (sometimes pet stores have the 40 lid in stock), make sure to get a reptile terrarium lid!

Similarly there are also Acrylic and wooden enclosures. You'll want them to have the ventilation on the lids or very high up on the sides to prevent them from attempting to escape, but I recommended looking into the brands Bucatstate, Niteangel, and Pawhut (before you buy though look for 'clones' of the cages by niteangel because you can find cheaper than their prices for almost everything they sell).

Wire Cage: These are awesome for allowing for hanging enrichment like toys and shelves, but chinese hamsters are very small so you need bar spacing of at most 3/8". The Prevue 528, Savic Hamster Heaven Metro, and Crittertrail Super Habitat are all awesome options! These can all be purchased online, but Petco sells the Crittertrail Super Habitat and the Hamster Heaven can also be purchased from many Pet Supermarket locations if you have those near you!

That's a Prevue 528 set up below!

Connectable Cages: If you were wanting a Syrian Hamster (also called golden hamster, teddy bear, black bear, fancy hamster, etc) these wouldn't be possible at all since the tubes cannot accommodate a syrian hamster, and they are honestly HELL to deal with because occasionally they'll pee in the tubes and you'll have to take it all apart to clean it, but you do technically have one option for connectable cages with dwarf hamsters if it interests you. The Crittertrail Super Habitat is about 500sq inches, and features 1 connection port. You can attach connectable cages to that as long as you can maintain them. You don't really want to do only small cages connected to each other, hamsters may be burrowers in the wild but they are also major explorers. If their entire enclosure simulates a burrow they will want to escape that burrow to explore. You want a large main enclosure to allow them to have a 'surface', and to give them the option to burrow on their own (the small ones never have enough room for bedding ugh). The pros to connectable cages is that you can have different areas that are easier to maintain, and chinese hamsters are quite agile so they tend to enjoy being able to explore. If you decide to ever use tubes in your cage, try not to have any straight up and down sections larger than 3-4 inches, if they fall within the tube from any higher they're able to get injured quite easily.

(sorry couldn't find many good set up pics for this option since this style of enclosure has fallen out of style in the last few years for easier, larger setups)