Rather depends what you're using it for, and what rest of build looks like. The FX is fairly c**p, but that i5 is last generation, and far from the best. If build is for gaming, GPU tends to be more important than CPU, in most cases, although i3 and better GPU isn't necessarily bad. If you have local Microcentre, they have good walk-in deals on Ivybridge i5's at the moment, so something like this might be a good value build, although would need to know more of your needs/ budget, to confirm if best option. Also, as you haven't said, I'm assuming you are in USA. PCPartPicker part list / Price breakdown by merchant / Benchmarks
If, as seems likely, OP is struggling with budget, my build only really works with access to Microcentre, and we don't even know if OP is in US. Without that, something like this might be an option, although not as versatile for all games. PCPartPicker part list / Price breakdown by merchant / Benchmarks
OP though is talking of going to FX4100 to save enough for next GPU up. FX4100 doesn't even get close to i3 Ivybridge, even heavilly overclocked, and taking everything into account, costs more. i3 would be better than that AND leave more room to get better GPU. Certainly 4300 may be better, but again, would cost more, by time you've overclocked to get half way decent perfomance, compared with i3-3220 and H77, even B75.
OP was also talking of going for an i5-2310, but that's a generation behind so you suggested the 3470 and/or i3-3220. I'm just doing the same for the AMD CPU.
The link to benchmarks I gave on my previous post had stock 4300 pitted against a stock 3220, and like I said it outperforms it on both games tested(Skyrim and Diablo 3), and even on other productivity things, so I don't think there's a need to OC to get half way performance. If anything, the i3 needs to be OC'd in the BCLK to keep up on the benches it lost.
The i3-3220 is $123.20, the FX-4300 is $129.00. The cost difference is barely a big margin when the 4300 has 2 Piledriver modules that somehow translates to 4 cores, while the i3 plainly has 2 cores.
Certainly agree that if you use FX4300 with basic mobo, and don't overclock, it's a similar cost option to i3-3220. As to performance, 4300 wins in multi-threaded apps, 3220 in single threaded apps. On the other hand, if OP has access to Microcentre, i5-3470 is viable. Since we don't know where OP is, or budget, or even what rig is to be used for, it's a bit difficult to decide what's best option. I fully accept 4300 MAY be.