Tigerci :
hang-the-9 :
If you don't have any of the parts, going to a new gen i5 and DDR4 is better, if you can at all get to that budget. It will enable your 960 to work without worrying about the CPU bottlenecking any games.
Only time it's really worth going with a last gen setup is if there are existing parts, or you are getting them cheap from a friend or something.
I can try save some more money for i5 but what's the diference between a DDR3 and a DDR4?
DDR4 is the newest RAM and that is the RAM that most motherboards for the new Intel CPUs use. I don't think there is any cost differences, or at least not enough to matter. You don't absolutely NEED an i5, but that would be better as a one-time purchase instead of getting the i3 then wishing you had better performance and spending the money twice. There is a $70-80 difference between the i3-6100 and the i5-6500. The 6400 model is also OK to get, it's just slightly under the 6500 in performance/cost ratio. The i3-6100 actually is the best bargain of those CPUs and will run games well, just will be a bit of a compromise. Since you are looking to get a GTX 960 video card, you would be happier overall with the i5, and you won't be thinking a week down the line "Man, wish I got the faster CPU". But don't feel bad about using the i3-6100 either, it's a good CPU.
Power supply has to go though, really it should be the first thing to build a system around, not an afterthought. Everything is powered by it, you have a crappy power supply, you are risking damage to every component if that thing blows up. Do a search for "power supply tier list", pick something from Tier 1 or 2, Tier 3 as the absolute least quality you want. The main differences between Tier 3 and the others is really parts used and detail, they are still OK power supplies. Like the difference between a Toyota and a Lexus, Toyota will run fine, but a Lexus is a level above.