Ok, I listed an ATX build, so no worries there. It would cost about 190 to upgrade the Cpu to an i5 for what I listed, but even if you don't, the i3 will flat out beat the Amd Cpu you listed, and will out-perform an 8370 in a lot of applications as well. You con't *need* a better cooler if you aren't overclocking, although it's not a bad idea.
If you prefer 7, that's your choice, but I'd highly recommend 8.1. Just download Classic Shell and you get the normal WinStart button. There are other cases out there, but this one is really good for the price. Again, this isn't an ITX or MATX build, it's an ATX build and heat won't be an issue.