Welcome to the fire! Hope you enjoy the game.
There is not an approved list, per se. Most CAS guns are fine for SASS, but there are exceptions and there are limitations to other organizations, like NCOWS, and you should do everything you can to check out other guns. You will find most folks are not only willing, but excited to let you try out their guns.
Regarding shotguns, single barrel breakopens are legal, in 20 or above. The SxS market is pretty flush, with the Baikal (Bounty Hunter) and the Stoeger, also the Stevens 311. Again, take a while to see what is out there. Also, buy the shotgun last, it is the easiest gun to loan out. And keep asking questions here.
There is a structure to the side matches. 22 matches are pretty common, but usually using CAS type guns.
Hope this helps!
Adios,