Intel is the better option given the budget. AMD offers more cores but Intel offers more bang with their processors. AMD is also pretty popular with gamers because of the price, AMD is considerably cheaper than Intel oriented stuff.
AMD A10 7850K is pretty good but the Intel I5-6400 is better. I would forget the I3s from Intel, there are bigger and better things out there and your going to want a quad core instead of a dual core for the things you will need it for. I3s has hyperthreading only, 2 cores 4 threads while the I5 have quad cores and hyper threading. Even the I7s are getting into the decent price range, depending on which models you look at.