You'll see a lot of advice that you should consider upping that budget. Not gonna lie, I would put value on a good subwoofer with infrasonic output.
Shaking windows can actually be a sign of distortion, not clean deep bass. I am not there to share my experience

so must rely on your own thoughts.
Probably the best bang for your buck would be Hsu Subwoofers. Other "favorites you will see recommended will be the usual bunch: SVS, Monolith (Monoprice), Rythmik... Even Klipsch is now putting out some good quality Subs.
...But in a room that size, you definitely want something large enough to help fill the space. Bass waves are very large and powerful, and the total open room volume will act on the subwoofer. Too small a Sub and you will need to turn it up louder than might be linear in good SQ and performance.
Regardless, I would say begin looking at the Hsu VTF2. I would recommend 2 of them, largely because you can place them more advantageously in your room to improve overall Bass quality, work against room modes, and improve output which will aid in keeping distortion down.
Other good option I think is one of the better performers will be the Monolith 12". I'd try to steer you to the 15, but that can be a hard sell, especially at the budget you have currently set.
Good quality Bass is a worthwhile investment!
