I understand, don't worry I don't see any glaring issues. Usually those problems result because an aftermarket CPU cooler is too tall or a $1000 GPU is too long. You have pretty normal sized pieces so I think you're good to go.
Here's the deal on the GPU situation. An RX 480 is brand-new and would no doubt dominate any game you want to play in 1080p at 60 FPS. However, as a brand-new offering they are hard to find, can be a bit overpriced, have loud and hot reference cooler designs, and often have some driver issues that can be annoying. If you're willing to deal with those problems a 4GB RX 480 (8gb isn't necessary for 1080p) is great. But if you want a simple solution, just opt for the 960 and go have fun.
Also I'd like to add my own personal experience with gaming boxes. I tend to buy mainstream GPUs in the 200-250 price range, like the GTX 960 or RX 480. There's good value there. Then every 3 years or so it starts holding me back in some games, so I buy another $200-$250 GPU. I can usually do that twice for one good processor/mobo. This way I always have my games being very playable, sometimes I have to turn down a few settings, no big deal, and I don't spend $500 on a GPU that I'll replace in 4 years for the same reasons anyway. BTW, if you save the GPU box and all the stuff it came with, you can sell it every couple of years when you upgrade, right now a used 3 year-old GTX 760 (~$250 new in 2013) sells for $100 on eBay.