Onboard graphics on AMD boards is NOT a problem, thats for sure. 780G, 785G, 790GX, all awesome performers.
The reason your GTS outperformed your 4870 is probably because you cpu was bottlenecking it.
Personally, I would stay away from Foxconn, ECS, Pc chips, etc.
Stay with Gigabyte, MSI, Asus.
The Cpu is a good choice.
Not sure about Sigma, I would go with a Corsair 650-750 w/5 yr warranty.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139005
DDR3 and AM3 board would be better for future upgradability, but sticking with your DDR2 and a AM2+ board would perform just as well.
22" is usually 1680x1050 which is pushing a single 4850 (512mb) on high settings in newer games. Games like STALKER CS, that game put a hurt on my computer. I had to turn down dynamic lighting and texture detail and AF just to not get dizzy.