The first run I made was out of 19 gauge wire. Even at only a foot in height, and a LOT of reinforcing, the sides will bow out under its own weight when I open the doors. If it were any taller, as I assume he would want for a pet cage, I don't think 19 gauge would be suitable at all.
14 gauge is definitely a lot sturdier, but also more expensive and harder to cut (especially if you're doing it by hand!) 1" x 1/2" 16 gauge is what I use for everything now, but that fits my needs as a breeder. For a pet cage, wider spacing would be okay, so long as the chin is big enough to not get its head stuck.