I always like a challenge, with your initial budget you can do okay with this:
99$ + ~15$*+h
Polk Audio MOMO MM2124
12" Single 4 ohms MOMO Series Subwoofer (MM 2124)
200$ + free *+h
Infinity Reference 611a
Mono subwoofer amplifier
456 watts RMS x 1
The sub is rated very conservatively, it'll rms well beyond what it says.
Hrm. . . with that, you'll still go a bit over on the box and cables unless you are able to DIY the box (cables aren't too bad). Since you're connecting to the factory head unit, you'll have a bit more fun since you'll have to run a filtered high pass to the amp, but with a little research, it'* pretty straight forward.
Now, for drop-your-jaw bass (on a budget), I'd go with this driver: http://www.sonicelectronix.com/item_...SR124-DVC.html
With the same infinity amp (it'll push 657rms into the dual voice coil), you'll get some pretty hefty "oomph" out of your system.