Olá rjcm -- I'm in an apartment too, and I haven't got on to finishing my guitar yet, so if any of the real experts here say something that disagrees with what I'm about to write, believe them and not me

But from what I've read, the best thing for people in our position is to use wipe-on or brush-on finishes rather than spray-on, because it's less likely to make a mess. One important thing to consider is where you're going to leave the parts while the finish dries. I'm lucky enough to have two bathrooms, and one of them is very well ventilated and has a beam where I can hang things, like this. Whatever way you use to apply the finish, you'll need something similar -- a well-ventilated and non-dusty space where the finish can dry. If you can't hang them up, the build guide has some clever ideas for supporting drying guitar bodies on pages 19 and 20.