I'm building a computer for the first time and I decided to go cheap ($20) on the case and it is only 190 mm wide (mid-tower size). The CPU cooler (Hyper 212 evo) I got is about 158 mm tall so I was told that it might not fit.
Will this work? I have an MSI motherboard and an AMD Oct-core Bulldozer 3.6 GHz CPU so I need to consider the spacing between the motherboard and the case and the motherboard+ CPU's width.
Also, the motherboard only has a PCI-2 slots while my graphics card is PCI-3. Will this hamper its benchmarks in any significant way (HD Radeon 7770)? I'm not too heavy with gaming so as long as it can play games like Fallout 3 or NV it'll be enough for me.
If the case doesn't have a side fan, it should fit (barely). I'm assuming that you're talking about a Hyper 212+/Evo and they require a case width of 7.26" and your case is a hair less than 7.5" wide. It'll be a very tight fit, though, even if there isn't a side fan.
As far as your GPU and mobo goes, you're fine there. Nothing to worry about. No current single 3.0 card is bottlenecked by a 2.0 slot and certainly not a low-mid end 7770.