Unless you're building an uber sli/crossfire setup, you can just buy a pre-built and then upgrade the Graphics card. I got a good deal on a Dell XPS 8500 for 500$ :
Processor: Intel Core 3rd Gen i7-3770 Processor
Dell Wireless 1703 802.11a/b/g/n, Bluetooth v4.0
1TB 7200 RPM SATA Hard Drive 6.0 Gb/s
AMD Radeon HD 7570 1GB GDDR5 with DVI and HDMI Ports
8 GB DDR3 SDRAM 1600MHz (2 DIMMs)
16X DVD +/- RW Drive
460W Power Supply
Upgraded the 7570 to a GTX 660 TI (300$) myself and this will run about anything on max settings at 1920x1200. The Graphics card is the most important thing on a system and shouldn't be skimp. i5 or i7 ivy bridge, they perform the same as far gaming goes. 8GB ram is enough for gaming too.
What do you recommend for monitors? How important is response time? And is 27 too big for a normal desk?
This is another factor, people only have higher end gaming system if the plan to game at 2560x1600 30" monitor. Those run at least 800$ by themselves. The cheaper 27 monitor are 1920×1080 or 1920x1200, why build an awesome gaming system if you're going to play on a cheap monitor?