ElvisOnTheMoon :
Would it make sense to get a 6300 intitially, and then upgrade to an 8350? It seems that the 6300 crushes the G3258 in almost all modern games, and this PC is for running primarily new releases (with a bit of Fallout New Vegas in the mix, which shouldn't be taxing at all). Also, I want to get as much out of this build as I can initially, and I want to get it as soon as humanly possible - an fx 6300 seems like a good price/performance CPU. Am I wrong?
It would not make sense to get a FX6300 then upgrade to a FX8350 (or FX8320, or FX 8370, or fX9590 either) None of them are enough of an improvement to be worth the money.
If you want to try and play modern games on an about $100 CPU, you have four choices worthy of consideration.
Intel G3258. Overclocked, it is fast and powerful, but it will not play many modern games well at all because it has only two cores and that is no longer enough. It's a great legacy processor for 'blast-from-the-past' games.
Intel i3 4160 Fast and powerful, two cores and Hyperthreading allows it to run all modern games, although it may not be powerful enough for the most intense multi-person situations and Ultra setting (especially population and sight distance). It has a viable upgrade path to something like the Xeon 1231v3. I'm not suggesting an i7 4790K because the original i3 motherboard may not support it properly.
AMD FX 6300. Overclocked, it is fast and powerful, and it's three modules allow it to play modern games. Even overclocked, it's modules are less powerful than the G3258 cores when overclocked. There will be more CPU heavy games where the settings might need to be turned down to achieve good performance. This is almost an obsolete CPU with no meaningful upgrade path.
AMD Athlon X4 860K Overclocked, it too is fast and powerful and it's modules are more modern and powerful than those in the FX 6300 (but it still has one Fetch and two decode, and one L2 cache shared by the two Int units and the one FP unit) Steamroller is faster and more efficient than Piledriver (in FX6300) so in many cases where two modules are enough the 860K may be superior. It is a more modern technology, but reaching the end of obsolescence, and there is not upgrade path at all.
I would eliminate both the G3258 and the FX6300 from consideration for what you are doing. The i3 is the good powerful choice with a future (of a sort), the 860K is the interesting budget choice (but you must overclock it)