no, the pentium won't slow down gaming performance.
either cpu would be fine with a hd 6770.
i personally prefer pentium as you can upgrade to a core i5 later on if you like.
if you go with athlon, you should select a good am3+motherboard that can support am3+ cpus.
Custom PC built a budget rig a while ago where they used a G620 (close enough) for the CPU. The rig was capable of playing Skyrim at 1080p with decent fps, so I would say go for the G630. As mentioned above, it also keeps open the option for upgrading in the future. Which the Athlon doesn't (or at least limits in comparison to the G630).
Thanks guys and I am thinking about the G630 because the board I am buying with it will support the Ivy Bridge then I'll upgrade! P.S the Pentium processor says that it supports up to DDR3 1066 RAM but the board says up to DDR3 1333 but I'm buying 4gb DDR3 1333! Well it underclock for the CPU or stay the same for the mobo???