It depends on the games you want to play. The i3 6100 is actually pretty capable at gaming and in a lot of cases comes in close to the i5. The advantage you get with the i5 vs the i3 is it is a true quad core (i3 is 2 cores with Hyper Threading, i5 is 4 cores no Hyper Threading, however as the cores are so wide the i3 is *almost* as fast), and it has turbo which the i3 lacks.
If anything, the i5 is a better longer term bet, but the i3 will probably do the job for now.
Edit: As I said though depends on the game. If you mainly wan to play lighter stuff like MOBAs then the i3 would be plenty. If you are wanting to get into the latest things the CPU can be more of an issue (e.g. Star Citizen is actually more CPU limited than GPU, for that...