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This will be in a small bedroom I am putting a projector screen in (14' x 12')
Based on those dimensions and depending on your ceiling height, I think you might be a bit disappointed in the monoprice at that power rating. I used an MK dual 12" push pull rated at 125w in a room not too much larger than that and it never lived up to my expectations. Running two subs is great for bass-o-holics but they have to be right for your space; two under-performing subs (in general) won't make things any more enjoyable than a single will.
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I have a 12 inch SVS sealed sub that works great but the price is a bit more than what you have listed. Saying that, I extremely pleased with the performance and my room is larger than what you have listed. Whenever I move home from Singapore I will not only convert the amp from 220v to 110v in the existing sub but will also buy from SVS again.
I know it's a little outside of what you are wanting to spend, but trust me when I say the conversation should start and end at SVS. I went through the previously mentioned MK, Velodine, HSU and a B&W 12" before finally purchasing a SVS PC-12+ (circa 2006) and there is simply no comparison. The SVS will absolutely annihilate nearly anything at it's price point and a lot of more expensive subs as well. They currently have a ported and non-ported box 12" with a 325w RMS amp that would probably do quite nicely in the space you described. You may also check the used market as people are always looking to upgrade their gear, and SV sometimes has some B-stock (returns & minor scratch-dent) at a lower price.
Finally, audition as much gear as you can get your hands on at your price point in person. There's nothing worse that getting home with something, hooking it up, and realizing that you are going to have to "settle" for it when you know you might have left better options on the table.