Is this CPU suitable for MSI GTX 970 4GB?

Solution
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).
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).
 
Solution
It is not a bad CPU, but I would suggest either getting the K version or something better.

Your best bet with computer components is to get the best possible, or near it. No you don't need one of the $1,000 Intel CPUs, but getting at least a K ("overclockable") processor is ideal.

I have a 6 year old, I repeat 6 year old i7 960 @4.1GHz with a 970 currently, and for the better part I can max out nearly every game with decent average in framerate. Quantum Break being the most intensive game on PC currently.

That CPU will be a bottleneck to your GPU since you won't be able to overclock it. And in the long run you will have to spend more money in different increments as opposed to a larger lump sum every few years.