What gauge fence post should I use for a 36" wide wooden gate?
Assuming that they are round metal poles that are generally used for chainlink, the 'corner' poles are what you generally use for a gate. You pretty much use corner poles anytime you terminate a run of any kind, and a gate opening is a termination. The actual gauge isn't going to matter so much as the diameter of the pole, you need to make sure your gate hardware will fit the pole. Since your are going with wood, the extra few bucks for the thicker gauge is probably worth it, the actual diameter should be about the same either way.

Also, make sure you measure the opening correctly before concreting the poles in.  Depending on the hardware you use you may need to leave extra space.  For pre-fabricated chainlink gates, you need something like 39 inches for a 36 inch gate.  Since you are using wood, I assume you are fabricating it yourself, but you'll still want to make sure you leave plenty of room.