Heavens, no. Please do not go spending your $1000 budget on that Polk setup. Especially not the subwoofer. Polk speakers are...o...k. But you can do so much better.
1) Get the Pioneer 2nd gen (model numbers all end with a "2") Andrew Jones speakers.
SP-FS52 towers for front left & right
SP-C22 Center
SP-BS22-LR bookshelf speakers for surrounds.
You can get them at Best Buy for $250/pair for the towers ($125 each), $100 for the Center, and $100/pair for the bookshelf surrounds.
If you want a slightly better price, tigerdirect.com is selling the
SP-FS52 towers for $100 each ($200 for a pair) - the price shows up at checkout. The
Center and pair of
bookshelf surrounds are the same $100 price as at Best Buy.
Unless you absolutely need 7 amp channels for some reason, there's no need for the AVR-1913. Instead, head on over to accessories4less.com and get a deal on the
AVR-1713 for $299.
accessories4less is a fully authorized Denon dealer. You get a full 1 year warranty. They simply sell clearance or refurbished units, which are good as new. This is absolutely the best place to buy a receiver.
The 1713 has all the same network features, AirPlay and inputs as the 1913. The 1713 actually has a BETTER "level" of Audyssey than the 1913. I know it's weird since the 1713 is a "lower" model number. But for two years in a row now, the 17xx model has gotten Audyssey MultEQ XT, while the 19xx model gets Audyssey MultEQ (one step down from MultEQ XT, despite being a higher model number). The only thing the 1713 gives up are two amp channels. The 1913 has 7 amp. The 1713 has 5. If you're only going to run a 5.1 speaker setup anyway, why pay more for the 1913 and take a step DOWN to Audyssey MultEQ while doing so?
If you really want AirPlay, network features and 7 amp channels, get the 1912 from accessories4less for the same $299 price as the 1713. It's basically identical to the 1913, so why pay $50 extra?
And if you don't care about AirPlay and network features, forget all of them and get the 1712 from A4L for $249! Weirdly, the 1712 has 7 amps AND MultEQ XT. It just gives up AirPlay and the network connection. So the 1712 is my favourite because it costs the least ($249), it had 7 amps if you want them, it has Audyssey MultEQ XT. And you can always add an AppleTV or a network streaming box later and do those things better than the built in versions in the 1713, 1912, or 1913!
So, if you take this advice and spend $400 on the 5 Pioneer speakers and $250 on the Denon AVR-1712 from A4L, you'll have $350 left to get a decent subwoofer.
Since you have a large room, the best option, IMO, is the
Klipsch Reference RW-12D on sale for $320 at newegg.com at the moment I'm writing this. Sale price there seems to fluctuate. Normally see it at $350. But it's a clearance model. Stock won't last long. It's a very decent subwoofer overall, but most important, it can handle your large room size in terms of output, AND it fits your budget perfectly.
This Pioneer, Denon, Klipsch package is the best ~$1000 5.1 package for a larger room by a country mile at the moment. There's never been an easier recommendation than this. I can't stress enough how much you should buy these particular products, given your budget and room size. Only possible question is the exact model of Denon receiver. I hope my description was clear enough for you to determine which one has the features you want.
Forget the Polks. Especially the Polk subwoofer. Get this package instead. You'll be VERY glad you did.