I agree that $200 is kind of tight. Here what I recommend..
Option one: Soniceletronix sells Image Dynamics IDQ12V3 subwoofers for around $250. In SQ department, they are among the best at any price, but for their price they're probably a value leader. Try to make sonic an offer of $200 for the 12 sub, see if they accept it. The sub is optimized for an average sealed box (e.g. 1 to 1.3 cu ft). Xmax is somewhere in the neighborhood of 16-18mm and the power handing is around 500-700watts RMS, which is good enough to produce loud bass, at least in a midsize car.
Option Two: Get one Infinity Kappa 120.9w. This is infinity's top subwoofer. From my experience, it sounds very nice and clean with better than average upper end extension, and low inductance. Unfortunately, I haven't had a chance to compare it to IDQV3. It's been said to compare favorably to IDQV2. xmax is 17mm. Power handing is "only" 350watts RMS, though it nowhere near reaching its xmax at this wattage. Optimal sealed box size is around 1.3 cu ft. It can be picked up for $150 or less shipped. The cool thing is that it has 2ohm/4ohm impedance switch. Should you want to add a second sub, you can flip the impedance and add a second sub to the same amplifier without affecting the final impedance load.
I would be leaning towards the option one. ID IDQV3 subs have tremendous reputation in SQ department. They had reportedly done well in car SQ competitions.
