If you are talking about a receiver, two speakers and a sub, you should be able to put together something decent for that amount.
Since you are in an apartment, you probably don't have a lot of space to fill so don't need a huge receiver. You could look into a stereo receiver or integrated amp with sub out but there probably aren't a ton of choices. I'd look into an entry level AVR, maybe a 5.1 receiver that has HDMI capability. You should be able to find something decent for under $500. Look into Onkyo or Yamaha for bang-for-buck.
The sub is the thing you don't want to skimp on. A cheap sub will give you one note bass. I don't have any specific recommendations. I might suggest something form Hsu Research but I'm sure others will weigh in with better suggestions.
With whatever is left, you should be able to get some decent monitors and stands or decent small towers. I'm a bigger fan of the former, especially where you don't have to fill a large area. There are lots of decent choices but I would look for something with a 5-6.5 inch woofer so you can cross to the sub at 80 Hz.
Jim