Well, to start, if you're going to spend proportionally more on any single item in your home theatre, the subwoofer is the place to make that out of proportion purchase. I've zero problem with the idea of the subwoofer costing a full 50% of your entire speaker budget. Get great Front L/R speakers. Just save up for a center and run the Front L/R in "phantom" center mode for a while if you have to. Don't worry too much about the surround speakers. But by golly, get yourself a great sub! Other than the Front L/R speakers, it's the most important speaker in your system IMO.
With that out of the way, I have to be honest and say that "small" subwoofers are not my forte. There's just no getting around physics, so it's extremely difficult to make a small subwoofer that still plays low, accurately and loud all at the same time. Thankfully, you have a small-to-medium sized room, so massively loud output isn't a priority. But it's still very difficult to make a small subwoofer reach down to those lovely 20Hz and below notes that add so much impact to movies.
Are you restricted in terms of the height of your subwoofer? I ask because one very good option would be to get a cylinder subwoofer such as the
SVSound PC12-NSD DSP . For your room size and budget, that would absolutely be my top recommendation for a subwoofer that takes up as little square footage as possible. Rather than being a big box, it makes up for its fairly small footprint by being tall. If going tall is an option, that's certainly the subwoofer I'd recommend the most to you.
If you can't go tall though, then things are a bit more tricky. There's the sealed
SVSound SB12-NSD . There's also the
Rythmik F12 , but the F12 is bigger, costs more, and sadly, Rythmik is having a bit of a backlog with amp stock right now, so it's on backorder for what might be a rather long stretch at the moment.
So honestly, in your situation, with your room size and budget, I'd be going SVSound. Get the PC12-NSD DSP if you afford the extra height. It does play lower and louder than the SB12-NSD. But if you have to have the small dimensions all around the SB12-NSD is about as good as you'll find.
Hope that helps!