In terms of gauge, just remember that the lower the number means the thicker/stronger the wire. So if you are at the store and there are two rolls of fencing with the same size holes, choose the one with the lower number gauge.
It depends what types of predators you have in your area. I use 2"x4" welded wire to keep out large predators like coyotes and bobcats and *hopefully* badgers which are my primary threats. The holes are on the large side however and something like a weasel could get in and a raccoon could...