There is no universal problem of bottlenecking. Some games or applications are relatively more CPU-intensive, and some are more GPU-intensive. Assuming you're gaming, the 7770 will be the limiting factor in basically any setting relative to any current CPU, except maybe at very low resolutions in certain games (but that's an invented problem). So, without knowing more--we need to know your motherboard if you have one, your intel/AMD preference, and your screen resolution--it's pretty hard to make a positive recommendation. OTOH, if your only criterion is that it not bottleneck your 7770, you can freely get pretty much any processor.
To be clear, it's not like pentium processors are so great. It's just that, for gaming purposes, you won't see much difference between a pentium and a core i7 when you're pairing it with a 7770. That's especially true at 1080p.
The biggest difference between the core i3 and the pentiums is that the pentiums don't have hyperthreading support. That will affect some general application scenarios, but it won't do too much in gaming; most games don't use more than two threads.
If you're going for a pentium, though, it's best to try to get as high a clock speed as possible. That could make a difference, especially in CPU-intensive games.