Hi, I am an Appleseed shoot boss and State Coordinator in Oklahoma. First off, I'm glad you are coming, and especially that you are bringing your wife. You will both have a lot of fun and learn a lot.
When it comes to your rifle, the most important thing is to bring an adjustable sling that will work with it. This is huge, since all the positions we teach are sling-supported field positions.
Other than that, you can get by just fine with about any kind of rifle. That being said, some rifles have certain features that make them a lot easier to shoot Expert with on the Army Qualification Test than others... and if you are wanting to buy your wife a rifle to use at the event, you might as well get her one that will give her the best chance of doing well.
While Expert scores have been shot with an AK, that is not exactly the ideal rifle for our course of fire and style of marksmanship, which is geared toward shooting consistently under 4 MOA from unsupported field positions, using rapid fire. Most AKs are mechanically capable of shooting to that level of marksmanship, but most shooters have a lot of trouble shooting them that well under such conditions.
Probably the AK's biggest problem is it's sights: they are notch sights rather than aperture, they have very short sight radius, and they are not easily adjustable. Also, the AK's factory sling was also not designed as a marksmanship aid. While it can be used as one, it is not ideal. AK's are also not particularly known for having great triggers.
The ideal rifle for the Appleseed course of fire would be a military pattern semi-automatic rifle with click-adjustable aperture sights, a generous sight radius, and 1 1/4" sling swivels on the bottom of the rifle so an M-1/M-14 GI web sling can be used.
I say "military pattern," because most military rifles are designed to be reloaded quickly, which helps with the timed stages. Your M-1 will be perfect (just make sure you have the right sling on it). An M-14 or AR would also be a great choice.
If your wife doesn't like the size and recoil of the M-1, I would say go with an AR-15 if you want her to have a center fire. They are light weight (as long as you don't get a heavy barreled one) and have light recoil. You might want to get one with a collapsible stock, so she can set it to whatever length is comfortable.
An AR would work great, but I am willing to bet that M-1 will grow on her after she learns how to properly support it with a solid position!
If you want to save money, you can use a .22 that is set up like a battle rifle, with Tech Sights, 1 1/4" sling swivels, and an M1/M-14 sling. The Marlin 795 and Ruger 10/22 are the most popular choices for this.
