Don’t assume that public school always translate to large classes. My daughter is at our state flagship. We are finding that many of her classes (actually most) are smaller than the classes I took at a small private college. Part of the reason is that some of the classes are honors which are smaller. She also had a lot of AP credit so she has few general education requirements. She also tends to pick out the more difficult courses which many student avoid. She is in a popular non-stem major so some classes are large. I was a stem major and my lecture classes were LARGE. I am also shock at how much she has been able to get to know her professors. So my point is that every state school is different but sometimes the stereotype view of large classes with no professor interaction is not always true. Talk to students in your field to see how it is at your state schools.
The difficult of getting your courses can be very true. Could also happen at smaller schools due to fewer sections.