The i3 -> i5 difference is a noticeable one when it comes to an application that's more CPU dependent.
Between the 4670k and the 4590. There is little difference between the two if you're not going to overclock. If you get the 4670k, even if you don't think you'll overclock, you might do it later on, so there's that option. It's not very hard to do either, just a bit time consuming.
But answering your question. The difference between the two i5 cpus is only the frequency I believe. There performance should be relatively the same. If you really don't plan on overclocking, then going with whatever's cheaper would be best.
1) The difference between 4670k and 4590 is totally negligible. You won't see much difference in gaming between them.
2) i5 4590 beats i3 4130 down with its awesome single core performance (Games require a good per-core performance). And Hence there is a good difference between them, when it comes to gaming processor.
3) Fat_Cat has provided a precise solution. i5 4670 flaunts an outstanding performance when it comes superior high end gaming.