Sleeper subs in the $500 range....

A Velodyne F-12 servo series (used) will be the best you can do for music. Just make sure it's in good shape. Response to 20hz and distortion under 1% at most playback levels. Limited ability for home theater in that size room but the winner for music.
Curt

with a 20x16 room don't get the small HSU VTF2 as I have heard this and it is very disappointing (lots of port noise, because it don't produce that much sub bass)

I have a Servo Velodyne F1800X and it is quite amazing. If you have an extra channel of amplification get a VMPS Standard or look at the SVS subs

Definitive Technologys ProSub 200
549.00 new.
Better in my opinion of the Velodynes within the same price range.

250rms, 12in driver, fantastic subwoofer.

I may get flamed, but I like the Klipsch RSW 12 or 15, which you should be able to find used for around $600 to $800