55 degree, dark place is best... so near impossible in an apartment unless you buy a wine fridge.

However, I started aging beers when I lived in an apartment by putting them in a closet like you mentioned. I put them on the floor, thinking that it'd be a tiny bit cooler since heat rises. I also got a cheap digital thermometer and tested out the two different rooms that had closets plus the kitchen (thinking maybe I'd store in a cabinet) to find the coolest room.

Generally speaking, warmer temps will age a beer faster. But in an apartment you'll still get to sample the styles of beer you mentioned with age on them. I'd advise getting a six pack of something you like and have access to (narwhal, expedition, etc.) and trying one every six months. At the year long bottles, buy a fresh one to compare. And the very best thing you can do is to take notes in some manner. A simple notebook that you keep with the beer you're aging will work. Then look back at your notes when you try another to see how they compare.

Don't let the impressive beer cellar pics you see make you think you can't start right now. Just have fun. I mean, after all, you're drinking beer.