Sleeper subs in the $500 range....

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

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

250rms, 12in driver, fantastic subwoofer.

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

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