The BIC F-12 is a very popular budget sub woofer. I own one and it has been a great purchase. In a large space like that, you aren't going to get significant bass from any sub under $600. Whichever you choose, make sure to place it correctly, you can get much better results with proper placement. Look up the "sub crawl" method for a good technique.
Samsung PN60F5300 | Denon DBP-1611 | Roku 3
Denon AVR-1713 | EMP E55Ti | EMP E56Ci | EMP E5Bi | BIC F-12
Topping TP23 | NHT SuperZero 2.0 | Velodyne DEQ-8R