This helps a lot.
You know, I hear many great things about the Energy Take 5 system.
I enjoy Energy speakers and these would even knock the socks off of Bose
Energy Take 5 (5-speakers for $179.00 shipped / no tax)
http://www.newegg.com/Product/Product.aspx?Item=N82E16882269004
*There are lots and lots of budget subs, but IMHO I never felt to skim on a good quality sub.
If I was on a budget I would take a look at these subwoofer's:
Acoustic Audio - $200 or less for the 12"
I hear these subs can go to a flat 20hz by one of the forum members @ bluray
http://shop.ebay.com/items/?_nkw=HD-SUB12&_sacat=0&_trksid=p3286.m270.l1313&_sop=12&_odkw=Acoustic+Audio+HD-SUB&_osacat=0
BIC America F12
Dayton Subwoofers - I woulden't shy away from these subs either. I wish I got to demo one.
http://www.parts-express.com/wizards/searchResults.cfm?srchExt=CAT&srchCat=620&CFID=507
As for receivers; so many out there from Pioneer, Onkyo, Sony & Yamaha.
Any of these with 60 watts x 5 (5.1) would do great and of couse still sound better then any Bose out there

Check on Craigslist and find a private local seller selling any of these speakers @ price ranges from $50-$500
A good one for about $100 from CL would be great. Make sure you get at least a 5.1 receiver and not 2-channel stereo.