There's a lot going on here, but there is one absolute fact that need to be recognized:
Gauge has absolutely no effect on recoil. All it does is typically set up the more important variables that effect recoil. Trying to narrow your search down by gauge is pointless, as it's sort of like saying "I'm going to buy a V8. Don't know what that engine's gonna be stuck in, but it's gonna be a V8!"
The argument that a 20 gauge will kick less is simply not true. What is true is that the 7/8 oz. loads typically fired out of a 20 gauge will kick less than the 1-1/8 oz. loads typically fired out of a 12 gauge. However, take that same 7/8 oz. of lead and accelerate it down a 12 bore barrel and you'll find that it's even softer to shoot. Why? Because a 12 gauge usually weighs more, and the mass of the gun soaks up more recoil energy. By extension, one could say that a 20 gauge actually recoils more, since firing a 1-1/8 oz load out of a 20 gauge will typically kick a lot more thanks to the gun's lighter weight.
In my admittedly limited experience (some of the guys I shoot with have been shooting longer than I've been alive!), it's always better to shoot lighter loads, especially if you're introducing a new shooter to the sport; it just helps prevent bad habits from forming. And with that in mind, it's worth taking a long hard look at the argument of semi-automatic vs an over under. On one hand, a semi-auto like a Beretta 390 or Remington 1100 will soak up additional recoil by bleeding off some of the hot gasses to operate the action, but they may not cycle the lightest of light loads like the reduced recoil loads from Remington and Winchester (both of which are damn close to .22LR recoil when fired out of my heavy over/under trap gun, by the way). In comparison, an over under may kick more, but will fire everything down to 3/4 of an ounce.
At 5'6" she'll need something with a shorter stock to move the balance closer to her body. Most shotguns are made around the old US Army standard sized man, which is quite a bit taller than that. Browning makes many of their guns in shorter sizes, and all over under's can be quite easily shortened by anyone with half a wit's worth of gunsmithing talent. But by all means, the best bet is to simply take her out to a shop, explain to the shopkeeper what you're trying to do, and start putting guns in her hands. She'll rapidly start to notice the difference!