I've bought 3 total PC's from ibuypower, I've found them to be of excellent quality, their service support professionals are indeed professional and know what they're doing (I can tell a good story if you want) and they're half decent in price.
This rig, with a 5770, should be fine for you. If you want a bit more future proofing, a 5850 would do just fine. Note that the price does in fact include Windows 7 home premium 64 bit too, so everything will be installed already when you get it and you just set it up and fire away.
Note that this will not come with a monitor, but will come with a mouse and keyboard and speakers. You can opt to NOT get them, but it only takes a few bucks off and I like to have spares : )
EDIT: I would like to add that my two current PC's are self built, but I bought the 3 from ibuypower a while back (before I was comfortable building my own). 1 for me, 1 for a friend, 1 for my own mom (lol).
IMO for $1000 get an AMD CPU, ~400-500W PSU, 5770 GPU 2x2GB DDR3 RAM... you have to do some research but you can probably do it for under $1000.
Anyway, there's a boatload of people with threads on exactly this is the "homebuilt PC" thread topic. Have a browse there to get some ideas what people are buying. If you want to buy a pre-built one, then again best thing for you to do is just shop around and compare.
I made a computer a while back for $800 just using combo deals in newegg...
it was something like this:
AMD Phenom II 720BE
Cheaper 4GB 1600MHz RAM
500GB WD Caviar Blue
Some cheap 1x16x PCI-e slot AM3 motherboard
Antec 650W PSU
And some good cheap case.. like an Antec Two-Hundred
And a $20 Dvd Burner
This is assuming you don't already have some of the components...
And this video card is way too much for your monitor.