What sub woofer to for this system & room?????????

Energy exL12.Used about 350.00.You'll have fun with this.Never worry about over woofing ,you can always lower it.

The only probable 10" "slimmer footprint" sub for that application would be one of the "cube" powered sub's (Sunfire, Velodyne, etc) or like NHT Sub 2, etc.
Any particular reason you want a "small footprint sub?"
With this level of system, you should likely stay in the lower price points, but you need more sub than you're hinting at possibibly. Are we talking about mostly HT dubties?...some music? I presume so. Anyway, a good deal on a sub with a lot of output for your money would be a used Def Tech PF15TL+, or new if you like.
If your budget is less, you should try to go to Best Buy(seriously), and maybe look at the lesser priced JBL woofers, which are pretty good actually. How much are you spending?
You could ofcourse go up in price, but you don't need to so much. For a minium, as a 10" woofer, you should consider maybe Paradigm PS1000, which is a great woofer(performs more like a 12-15" sealed woofer for output, musicality, etc. What is your budget?

Suggest you get at least a 12" or you won't be really "Woofin'"

try the bottom of the line NHT or a HSU Research. Both were very good in their day and reasonably priced.