Hang on to your hat. Your about to get a truck load of info.
First and best advice will be to get yourself and your wife to a range to test fire as many different handguns as they will rent to you, in as many different calibers (but stay away from .50's for now).
.22 seems to be easy to shoot, and a good place to start, especially if you know it will only be your first gun.
If you are looking at semiautos:
Bersa .380 seems to be real popular, inexpensive gun that most women can handle, and is a little better in the self-defense arena.
Anything 9mm is a step up in terms of self-defense and recoil. It is probably the cheapest ammo (aside from .22's) to buy, and something to consider if you plan on practicinig a lot and getting good.
.40 caliber is popular with police agencies right now. It has a bit more "snap" and recoil.
Don't be afraid to try shooting .45 ACP.
Some will point you toward revolvers, as well. Revolvers tend to be easy to understand, easy to maintain, and very reliable.
I would stay away from a snub-nosed for now, because they can have a lot of recoil.
Lots more to come.
Good luck, and enjoy the hunt!