I would also add multiple (at least two, preferably four) subs along each wall midpoint. Obviously given the size of the room, you don’t need anything super powerful, in my 12x11 bedroom a single Dayton sub 1000 manages a max of 110dB due to the ridiculous amount of room gain you get from a small room. With the dimensions being both small and square you’re likely to have some serious bass issues. With a single sub and the seating near the back wall, I wouldn’t be surprised if you ended up with a big 12dB hump at about 50hz, 4 Dayton sub 1000s will put you back $400 but will work wonders in helping to cancel out the peaks and nulls you’re likely to experience. 2 subs, one in the middle of the front wall and one at the rear wall would work too if you want to allocate more budget to speakers. If space is a concern, a sub 1000l is low profile and will keep out of the way.
Another sub option would be a few RSL speedwoofers, I don’t have any experience with them, but they’re cheap and have excellent reviews, should dig a little deeper than the Daytons too. You’re going to have to spend some time playing with placement if only two subs are used to get a decent response.
You said you don’t want “big” speakers, bookshelf speakers aren’t always small, in fact, many can be quite large. It would help if you better defined how big is too big.
The speakers recommended by others are all good choices, however I will add my own personal recommendations, with saving enough budget for multiple subs in mind.
For small speakers that will both fit into your budget and manage to hold up to the dynamic demands of home theater, I’d recommend 3 pairs of these, use one as a center channel
https://m.ebay.com/itm/Klipsch-R-14M-Reference-Series-Bookshelf-Speakers-Pair-/282625802331?epid=530092056&hash=item41cdcf805b:g:6w8AAOSwjDZYeS24&_trkparms=pageci%3A3ba17dec-a272-11e7-9cfb-74dbd180715f%7Cparentrq%3Abc6b85d415e0aa47cc741a5dffc8e55b%7Ciid%3A18
They should achieve an in room response of 70hz, which will allow a crossover point of 80hz. The horns will help keep the sound from spraying all over the walls and ceiling, which is a plus in your less than ideal room, and should have no issue getting plenty loud without distorting or compression of dynamics. The price will also allow you to allocate more budget to better multiple subs, which again, I strongly recommend in your situation unless you want boomy one note bass.
If you can go a bit bigger, I’d use these for the fronts,
https://m.ebay.com/itm/Klipsch-R-15M-Bookshelf-Speakers-PAIR-/371930498702?epid=1930203848&hash=item5698c9068e:g:HcIAAOSwB-1Yp2wT&_trkparms=pageci%3A63ec0e20-a274-11e7-b5d5-74dbd18043ca%7Cparentrq%3Abc79a94b15e0ab156abb2f31ffcf0e7d%7Ciid%3A3 and pair the above mentioned speakers for the surrounds. At the price the open box sell for, they really are a steal. Add this in for the center
https://m.ebay.com/itm/Klipsch-R-25C-Reference-Dual-5-1-4-Center-Channel-Speaker-Black-R25C-/142512422429?epid=1929792902&hash=item212e66fe1d:g:q-sAAOSwuOxZwTA7&_trkparms=pageci%3A4447f87a-a275-11e7-b5d5-74dbd18043ca%7Cparentrq%3Abc7f677d15e0ab4508ca3262ffe8571f%7Ciid%3A1
All 5 speakers with an R-15m, R-25c, and R-14m setup at open box prices totals up to about $550, leaving a grand for the subs. An all R-14m setup at open box prices would run about $450
You did not mention what size limitations you have as far as subwoofers go. It would help if you could elaborate. If four subs are used, you could play around with using a higher xover, as high as 120hz, this may result in smoother bass response in both the sub bass and the mid bass.
If you decide to go for a single better sub, or two better subs, assuming the seating is confined to a small around (ie a single sofa), I’d place the sub along the front wall (or front and rear wall for dual subs) and use a minidsp to eq the response flat at the MLP. With a grand being left for subs, you could also go for two SVS SB 1000. Being sealed, it should offer a faster step response than a ported sub with less resonance, which will give it less time to excite room modes.
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