Yes, i5 is faster, but it's also much more expensive. Also, that might be the truth that it's better to get a better CPU first, and then upgrade the graphics card, but only if you're willing to upgrade, and most people aren't. The OP has limited budget, and he cannot get everything the best. That's why you got to compromise. He will not want to spend over his maximum budget and have to still upgrade the graphics card.
My link shows that the Pentium is faster than anything AMD has to offer, so it will without a problems work for all games. There are many people who play with AMD CPUs just fine. Also, that benchmark was done with HD 7970, which shows that the CPU will not bottleneck even the best of the GPUs (it will limit them a bit on some games, though).