You could actually save even more with going with the fx 8320 and overclocking it to 8350 levels, you don't have to, it boosts to 4ghz on it's own, the 8350 is just at 4ghz at stock and boosts to 4.2ghz
with the money saved from going the 8350 if you'll be able to get the gtx 770 then sure go ahead, but in CPU intensive games you'll suffer a little, the Piledrivers aren't THAT bad, but, Intel is still better but I really understand about being on a budget.
If you don't feel like overclocking, get the 8350 and call it a day. BUT get a good motherboard like Asus r2.0 970 chipset (NOT LE version, doesn't have VRM heatsinks)
Many people have come to this forum crying that their CPU is being throttled and the problem ends up being their sucky AMD motherboard.
Here's a link. You'll want to get a 990FX motherboard if you ever want to crossfire/SLI your GPU though, 970 cripples the 2nd card at 4x speed. But it's fine for just a single GPU
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131873
if you want crossfire/SLI, get this one
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131851
hope I helped, and with whatever you go with I hope you enjoy your new pc, it'll pay for itself very quickly due to all the cheap PC game sale sites out there including Steam,etc...so don't feel bad about splurging a little and enjoy yourself, building a pc was the best decision I ever made