31 by 17 room - 5.1 system, looking to stay under $1750

Most HTiB systems you'll find will have limitations right away.
By way of example, many on this forum have spent your entire budget on just the Front speakers alone.
I'd suggest less buyers remose down the road by saving a few xtra dollars and buying seperates preferably by shopping on sale for a decent 5.1 experience.

I don't want gainiac's post to deter you from it altogether. I was able via different deals to get all of my 7.1 audio done for a little less than what you plan on spending. Granted some of it was model closeout, etc. but I got my Energy C series 5.0 setup for $399, added two C series side surrounds for $200, SVS PB series sub for $450, and an Onkyo 806 receiver for about $500. You can do it, but you need to be patient and look out for the deals. Trust me you'll be much more satisfied at the end result!

I am building my home theater on pretty much the same budget. Here's the setup that I decided on.

Receiver-Denon 1613 AVR $400
Front Left/Right-Polk Tsi 300 $378
Center-Polk CS10 $120
Rear Left/Right-Polk Rc85i $170
Sub-2 Bic V1020 $270 ($135 each)

Total $1338

I decided to go with 2 subs instead of one but you would still have a few hundred left for a blu ray player and a remote. Good luck and let us know what you decide to get.

A plethora of subs is the proper way to go in order to handle room modes and nulls.

My recommendations:

Energy Take 5.1 (can be had for under $400)
Pioneer vsx1022 (can be had for around $300)
Ps3 ($200)

All for under $1000.00.

I've owned bose...they simply aren't worth the money. The energy take 5.1 is far and away better and 1/5 the price. For a home theater and media room, the ps3 is still the best investment around--constant updates, flexibility, and if you read up on the sound settings (other threads), you can pass full hd audio to your receiver.

I just set this up for my friend's living room (we also setup a dedicated home theater with a really nice axiom setup)...the energys are amazing, even when you listen to them after the axioms.

You have a very large space, I would look for some efficient and dynamic speakers (which the Bose is not).

These are on a tremendous sale, and hard to pass up ($400 per pair):
http://www.newegg.com/Product/Product.aspx?Item=N82E16882156011

This matching center channel ($400):
http://www.kefdirect.com/iq60c-center-channel.html

These for surround ($200 per pair):
http://www.kefdirect.com/c1-bookshelf-loudspeaker.html

This subwoofer ($300):
http://www.newegg.com/Product/Product.aspx?Item=N82E16882780078

Total for 5.1 speakers = 1300

Then this receiver for $280:
http://www.amazon.com/Denon-AVR-1612-Channel-Theater-Receiver/dp/B004U403WM/ref=sr_1_3?ie=UTF8&qid=1346441071&sr=8-3&keywords=denon

This Blu-Ray player ($114)
http://www.amazon.com/Panasonic-DMP-BDT220-Integrated-Blu-ray-Player/dp/B00752R4PK/ref=sr_1_1?s=electronics&ie=UTF8&qid=1346441125&sr=1-1&keywords=panasonic+blu-ray+player

Then this remote (around $55 shipped):
http://www.bhphotovideo.com/bnh/controller/home?O=&sku=833606&Q=&is=REG&A=details

Right on budget

^^^^^^^^^ I second that especially the KEF