Personally, I'm running:
-970 Black Edition
-XFX 6950
-8 GB DDR3 1600 RAM
-750 Watt PSU
-1 TB 7200 RPM 32 MB Cache HDD
I get inbetween 190-230 FPS, even in team fights. I built it myself, cost me ~660. Picked up the 6950 and 970 on sale. Building it yourself really saves you a ton of money and is rather simple. Newegg even has tutorials on it. Definitely go with AMD if you're on a tight budget. i7's may be godly, but you'd be bottlenecking them without an appropriate GPU. If you really don't feel comfortable with building your own computer, get the prebuilt Son Golin linked.
One of my friends has something similar to it(it's got a X4 955 instead of an X6 1045T). He has the same GPU and same RAM. I think he gets ~70 FPS on max settings on LoL. It's a good startup build.