That more information on the PSU is needed has already been stated, so I'll wait for a reply on that before making a judgement.
Before anything else, I have to ask if you are going to overclock. If not, then the stock CPU cooler will be ok, although maybe a bit loud. If you will overclock, then even an inexpensive aftermerket cooler such as the 212 Evo or the Zalman Optima would be a significant improvement over the stock cooler.
It is true that the FX-8320, especially without being overclocked, can and will hinder the GTX 970 in some games. With that said, it will still play any game very well.
I would not spend as much on a case, but that is my personal preference. If you wanted to get an i5, then as coops1 said, getting a cheaper case would give your budget enough room to do so.