well the first two are 2 core chips. This means while you may be able to run some games well, there are others that will take a big processor hit because they don;t have the full 4 cores to play with. This is a big argument for the i5.
if you;re willing to give up the other two cores in the name of savings, here is a review of them compared http://www.cpu-world.com/Compare/291/Intel_Core_i3_i3-4130_vs_Intel_Pentium_Dual-Core_G3220.html
. The difference is not gigantic, particularly in graphics, which is what you seem to care about, so I would toss the i3 myself. That just leaves the other two. That comparison is here http://www.cpu-world.com/Compare/298/Intel_Core_i5_i5-4430_vs_Intel_Pentium_Dual-Core_G3220.html
. Again in games with two threads of less there is very little difference. That does not comprise all games though.
What the i5 will do is run more than one program at once far far better than the pentium. If you want to run the game AND have a browser open in the background or some such, or if you want to play games that actually have 4 working threads, you want the i5.
The question is do you want it enough to spend 3 times the money?