1- SAFETY SAFETY SAFETY!!! I agree, take a hunter ed course.
2- SAFETY SAFETY SAFETY!!! Take an NRA rifle or shotgun course. The NRA teaches proper shooting skills (and SAFETY!); whereas, the hunter ed courses teach safety in the field. Hunter ed doesn't teach how to shoot, the NRA doesn't teach field skills. You need both.
3- I believe a .22 rifle would be your best first gun. They are wonderful to learn on, and you'll keep shooting it for the rest of your life. It's easier to learn rifles first and then learn shotguns later, rather than the other way around. They are shot very differently! Shotgun shooters have a tendency to jerk the heck out of rifle triggers when they're first learning rifles. I also disagree with a poster who suggested hunting squirrels with a 12 gauge and #6 shot. That load would blow a tiny squirrel to smithereens, unless your squirrels are the same size as a fox! In fact, I used to use that load to hunt pheasants (haven't hunted pheasant since I moved to Colorado).
4- Lastly, thank your wife for her service, but keep this in mind (and don't tell her I said it): After 16 years of military service (and continuing as a Reservist), five years as a cop, and 10 years as an NRA firearms instructor I've come to one conclusion. There are two groups of people who carry guns everyday professionally, and the same two groups of people scare the piss out of me with their gun safety: Cops and soldiers! Your wife may be able to shoot 40/40 on the M16 qualification course, but if all she knows about gun safety is what the Army taught her then she's probably dangerous. We (the Army) are failing. As an NRA instructor, I give the Army a big, fat "F" on safety. Take the NRA course and bring your wife, too.