I am a college student and I have 2 chinchillas in an average sized 2BR apartment. They are great pets to have in an apartment because they are fairly quiet, you don't have to take them outside, and smell is not really an issue as long as you keep up a very simple cleaning routine. I found that filling the whole cage pans with bedding was far too annoying and wasteful to change all the time so my routine is as follows:
I have a double level Ferret Nation cage 182 with metal Bass Equipment pans. I have 3 sets of fleece pan liners that I made myself and I tuck them in around the edges of the pans so that usually no pee or poops get onto the pan itself (except when they tug up the fleece). I also have two Pyrex dishes (one on each level) filled with aspen wood litter and they usually contain their pee to those.
Once a week I will wrap the dirty fleece liners into a ball (with all the poops and hay and aspen shavings on the inside) and I put them into a plastic bag. I then use a little shop vac and vacuum up any excess poops from the cage pans and the shelves. I put the new, clean liners into the cage and I change the bedding in the litter pans. I take the bag with the dirty liners out to my building's dumpster and shake them out over the dumpster, bring them back in and toss them directly in the wash. It works really well as a system and there is never a bad smell. When I do all this I also take a cup with a little bit of white vinegar mixed with water and dip a paper towel in that to clean their metal flying saucer and any pee spots that have gotten on the cage pans, I then dry it all down before putting the new fleece in.
Other than that the only real cleaning I need to do is picking up stray hay and poops that have fallen out of the cage but if you keep on top of that and you do it once or twice a day (it takes like 3 minutes for my one cage) then it is really easy and manageable.
Something that you should think about for out of cage play time:
I have a small pet play pen that I open up and section off one area of my room near their cage for them to come out and play in. I learned VERY quickly that they love to chew baseboards and wires and absolutely anything so, I bought some more no pill fleece and cut it into approximately 8 inch wide strips that I have tacked over any areas of baseboard that they have access to in their play area. That has stayed in place for around a year and now they don't even bother trying to chew it. For wires and other things you don't want chewed, just make sure they are out of the way of the play area or you cover them with cardboard.
Overall, chinchillas are awesome pets to have in an apartment! I love my chinnies