To the best of my knowledge you don't get compatibility issues with CPUs and GPUs.
With regards to the i7-4790, it is a great processor but is probably more powerful than necessary for the vast majority of games (normally would only get i7 if you are doing CPU intensive tasks other than gaming or money is no object for your build). When you are on a budget you are usually better getting an i5 of the same generation, which is also a great processor. The benefit is you save money which you can put towards upgrading another component (usually the GPU).