Do you have a monitor? Of course you do get more power from building the computer yourself and it's really not that hard but all up to you.
I just browsed the computers on newegg.com. I'm not american (you never said where you were from so I will just assume you are that) so I don't know of other sites which sells prebuilt pcs. http://www.newegg.com/Product/Product.aspx?Item=N82E16883229285
This one had the best gpu out of the ones less than 650 as far as I can tell, and it's also a quadcore. Intel typically has better processors than AMD, which this is. But it will still be more than enough for gaming and everyday tasks. You also get 8gb of ram which should last you quite a while.
All in all this computer should be fine for years if you just avoid the highest settings.
You should wait for more input as someone might very well find you a better choice, even if this one is not bad at all.