As others have said, a good Rem 1100, 11-87, Beretta 390 /391 or something similar. Gas operated shotguns siphon off some of the gas from the spent shell to eject and load a new shell. That makes them have less recoil. Since she is a little thing, stay away from the 12. Can she shoot it? Sure. But it hurts after a while. Fun is probably way too heavy and long for her to handle well.
20 ga is very popular and you find it just about everywhere. 16, 28, and .410 have less recoil than the 12, bit shells are gonna be more expensive... Like 2 or 3x that of a popular 20 ga.
Real cool that your wife is into it. Make it fun for her and enjoy your time in the field together.