You gave some good info for the gang to assist you you in your quest. But, a few more questions need to be answered.
One, how long do you expect to be in your apt?
Do you have people above or below you?
What type of amplification are you using?
Now, based upon what you have told us so far, a 5.1 system IMHO, is plenty based on your room size. Being in an apt. you'll be limited on how much you can crank your sub, so I'd be tempted to save $$ there and use just a single 8 inch.
First possibility would be the EMP E5Ti, E5Bi, E5Ci, E10 sub, for $1320. You can save $250 by switching the towers for a second pair of bookshelves. Or, skip the sub.
A second choice is the Aperion 4T, 4B, 4C, and Brauvus 8A sub, together it's $1400. You can change the 4T towers for 4B bookshelves and that will put you just above $1k.