Whatever sub you get, I recommend you use near field placement, that means placing it close to your listening positions like a endtable or something. There are two big reasons for this. First of all, you have a large space with a small budget, and no $500 sub will completely energize that whole space, but if you go with near field placement, you won't need to pressurize the whole room to hear bass. Second reason is neighbors, for near field placement you don't have to have the sub turned up loud to hear some nice bass, but if you place it on the other end of the room, you will need to turn it up louder to hear it, but so will your neighbors, especially since you have concrete floors with people living above you.
With that being said, the subs I would look at in your price range are the Emotiva Ultra Sub 12, , Hsu Research VTF1, and Elemental Designs A2-350 or A2-300. All are under 500 shipped.
With that being said, the subs I would look at in your price range are the Emotiva Ultra Sub 12, , Hsu Research VTF1, and Elemental Designs A2-350 or A2-300. All are under 500 shipped.