I'm going to assume that you live in the USA (i.e. Newegg links will be OK) and that your monitor is running at 1680x1050 (i.e. a 20" or 22").
Since it's a gaming PC, start with the video card. The best thing you can afford on your budget is the HD 4870 X2. That is, your budget allows you to get the best video card on the market today. The Sapphire version is $520 today, the Visiontek is $530, and I prefer these to the other brands.
The next thing is to pick a CPU. For games other than FSX, a quad core is usually wasted i.e. two or 3 cores sit idle. I'd pick an E8500.
Next step is to pick a motherboard that works with the GPU/CPU. With that video card you don't need to consider SLi/Crossfire so a simple and cheap P45 will do nicely.
The P5Q Pro at $100 or GA-EP45-UD3R at $105 are good, for example.
RAM: get 2x2GB DDR2-800. Less would result in very low minimum fps. More would be largely unused.
Here's a good set:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820146731
HDD: WD 640GB is $75
DVD burner: SH-S223Q for example
Case/PSU: these depend on the choice of video card mostly, and of course personal taste. The PSu could be a 750TX or Silencer 750W, around $100. Cases could be Antec 900 or NZXT Tempest ($90) or RC-690 ($75). The first two have blue lights, the RC-690 doesn't.
You don't really need an aftermarket cooler, a sound card or a network card or a floppy drive and so on.
GPU $530
CPU $190
MB $100
RAM $40
HDD $75
DVD $30
PSU $100
Case $90
Total about $1155.
Edit: "upgrade in the future"... Actually, you can't do that unless you buy an X58 motherboard and an i7 processor and DDR3. But then your budget for the video card goes from $530 to $100 or so because those parts are very expensive, and your gaming machine would be garbage. Or you'd have to cut corners on case and PSU and you'd end up with overheating and damaged parts.
I'm all in favor of the i7/x58 but you'd need a budget around $2000 IMO to do it properly. Maybe later when prices drop...
The upgrades you can do with the setup I proposed is to replace the E8500 with a Q9550 if you ever want a quad, and to add hard disks and more RAM if needed, but that's about it.
Getting an AMD MB and CPU would have the same problem, because they're changing sockets too, to AM3.