I was in the same boat when I decided going PC for the first time. I went with home built and am glad I did. You can get a great PC from prebuilt manufacturers like ibuypower or cyberpower but its going to cost you more. You also lose out on the expereince of building your machine which is half the fun. You will save money building it yourself and its only going to benefit you to build it yourself. Then you will know exactly whats going on inside your computer and how to troubleshoot in the future.
There really is no reason to go AMD unless you are on a tight budget. Intel will crush anything AMD has to offer. Even AMD's six cores are about the same as 1155 quads from Intel. That's how far behind the tech is on AMD. If you decide to go Intel you should invest in a Z68 but since you are on a budget of ~1K you can grab a P67 if you wish to invest more on a GPU.
Grab an i5-2500K processor since you will just be gaming and doing everyday stuff on your machine. There are other variants of the i5 but they are locked and can't or will be much harder to overclock. Core i7's are for technical work which you most likely aren't into and won't be worth the investment especially on your budget.
RAM is RAM really and its going pretty cheap nowadays. You can grab 8GB of RAM if you want since its going as much as 4GB of RAM last year. 4GB will do the job but since its so cheap now you mine as well grab an 8GB pack.
GPU is entirely a personal choice. Some people stick with NVIDIA their entire lives while others claim AMD is the way to go. It really doesn't matter as they both do the same job. NVIDIA has more technologies which you can benefit from but its going to cost you $30 more the same performance an AMD card will give you. Also in my experience AMD/ATI cards run much cooler, have less power demands, and can run 3 monitors on one card while NVIDIA needs 2 cards running SLI to run multiple monitors.
Make a list on Newegg or whatever site you like and we can help you out with it. Its best to pick the parts yourself and have someone on here edit it a bit. Otherwise you just grab parts other people tell you and thats not really the best way to go about it.
Those are heavily CPU dependent games and any Intel SB i core processor will be faster than any AMD processor. The i5-2400/i5-2500K would be great choices depending on if you want to overclock and will destroy any AMD setup as suggested above. You really don't need to overclock at all in games with these processors.
If you can afford to spend this much on a PC 8GB of RAM is a no brainer (6GB would be tri-channel for LGA1366).
I prefer nvidia cards. They usually draw more power (at load) but run cooler. AMD CCC is just bad.
By the way you can get an i7-2600 and hackintosh it. That was obliterate your Mac.