You may seriously want to consider a receiver. Check out the Marantz SR4023 or the Cambridge Topaz SR10. They are both $499. You might be able to find them a touch cheaper.

The issue then is $700 of speakers. Right now, Crutchfield has the PSB Image T6 for $319 each but they are scratch and dent. That is a great speaker at a killer price but they are cosmetically flawed. You could also consider the Polk TSx440T at $349 each.

Alternatively, there are a couple at $399 each. The new Infinity Reference R253s and the Wharfedale Diamond 10.4. At $750, the Monitor Audio Bronzes are a great speaker.

IMO, the PSB Image's are the best speakers, especially at that price. Call and see if they can describe the cosmetic issue. Might be no big deal. Next best are the Wharfeldale Diamonds.

I would start with the Music Hall 15.3 amplifier. It runs $550 and is an excellent amplifier with enough power to run most speakers in your room.

Amazon has limited quantities of the Pioneer FS-51 tower speakers for only $200 per pair, and these are very good speakers that should work well for you.

If those run out, the newer model, the FS-52 should also be affordable. These are much better speakers than most in their price range; very impressive.

There are no floor-standing speakers for under $1000 per pair that are going to give you a substantial amount of really low bass; for that you will need a subwoofer.

The Pioneer speakers may have the bass you want. They have decent bass down to around 50 Hz.

If you get them, and they do not, then there is money in the budget for a decent subwoofer.

The Klipsch SUB12-HG is $300 from Amazon, and that would be my recommendation.

Whenever you're on a tight budget, consider used stuff on Audiogon and eBay. It might take time for a real bargain to appear, but you never know.

That said, you really can't go wrong with NAD for lower-cost electronics ($550). NAD will generally give you the most "punch for your buck." http://www.audioadvisor.com/NAD-C-326BEE-Stereo-Integrated-Amplifier/productinfo/NAC326BEE/#.U9gFR_ldUWI

That would leave you around $650 for speakers. Commysman listed a few good ones. I really suggest you audition any speaker before you buy them. NAD and PSB are owned by the same company, so there is some dealer crossover. But any dealer that's selling the brands we're suggesting will have good items to pair them with. (If you're near Maine, try Longplayer Stereo. Ask for my old boss/proprietor Rich.)

If local auditioning really isn't an option, NAD + PSB would work and both are readily available online at places like AudioAdvisor.com.