Watch out for "toy" subs (those marketed with desktop/computer speakers, or mass marketed - big box stores). Most of those don't go deep and the quality of bass is poor (flabby, one note, and/or lack definition).
On the other hand, be careful of overloading a small room (rather hard to do if you buy quality and stay in your stated budget) with really deep bass.
At your budget, powered is the only way to go (passive would be OK if you were going with multiple subs - a recommended approach - as the cost of one multiple channel amplifier could be cheaper than using separate amps in each sub and would cut down on all those power cords).
