I read a little bit about bottlenecking. I don't really get it :x
Would a dual core i3 at 3.3 Ghz bottleneck the Sapphire 7770?
It's possible, but you'd have to search around.
All I know about the i series is that they're very powerful for their core number and clock speed, but the i3 doesn't have a suitable architecture for gaming in the first place, it was made more as a workstation chip as far as what I've read has said.
I don't use intel processors though, so I wouldn't know personally.
Edit; I looked up the i3 you are most likely using and it's passmark index is very slightly higher than my Phenom II, but I don't know how it's architecture would perform in higher-end games.
Chances are that you have nothing to worry about, though
It wouldn't bottleneck, but apparently the bulldozers have worse or only slightly better performance when compared to their Phenom II counterparts, again I have no personal experience so you'd have to look it up yourself.
If you want something better than a Phenom II then I'd suggest looking into buying a new motherboard and getting an i5, an i5 should outperform a Phenom II without much difficulty, but I'm not sure so you'd have to look at benchmarks.
That being said, my Phenom II x4 965 BE is a beast of a processor for the price and it is very easy to overclock thanks to the unlocked multiplier, and it'll fit any AM3 slot, the only problem is that it has a TDP of 125w, so you'd need a decent cooler for it, I could give you at least one recommendation in that field though
I'm sorry if none of my advice is particularly concrete, but I only have experience with things I've used so the most I can do is assume and point you guys in the right directions