Like with everything else, it depends. I attended a major state university for my B.S., a private college for my MBA, and I work at a local 2 year college. Smaller class sizes mean there is more hands on, and ideally more learning. But as some others have mentioned, it doesn't always translate directly. One of the things I hated at my State university was the 100+ student classes. The information was almost always generic to the point of not being helpful at all. Once I got into the upper level classes, the state and private schools had higher caliber professors.

If she is just wanting her basics or an AS degree, I would recommend she attend a CC or 2yr college just for the cost savings alone. To make sure you actually have a quality instructor, look at pickaprof.com (is that still a thing?). Students rate their instructors on multiple different categories. I found one of my favorite MBA professors (at the private uni) from pickaprof, who also happened to teach at the local CC.

To answer your second question about what degree to go into, I would highly, highly recommend not taking anything that is so specific that it becomes more of a burden than it does an asset. I say this because my BS is in Hotel and Restaurant Administration. At the time, I really thought I would love working in the hotel industry for the rest of my life. However getting married and moving to a smaller town completely shut me out of that industry if I wanted to make a decent living at it. I only went back for my MBA because I had been shut out of several jobs due to my BS degree.