If you really value faculty involvement etc, I might suggest focusing on finding out those statistics directly and getting a sense of what current student experiences are like. That's as opposed to relying on a proxy like student/faculty ratios, low rankings or being a state school. Each state runs its own state schools (and some cities like NY have their own) and have wildly different levels of funding and support for education. And being public does not make them immune from going the adjunct all the way route.

Student faculty ratios can be reported using "full time equivalent" faculty. Meaning, your class of less than 20 students might not have a more available professor, because they're actually also teaching at 2 other universities in the same system to make ends meet. It's not the ratio to the number of tenured faculty, adjuncts count.

For class size, you can have dozens of small classes nobody takes, and have giant lectures for the core intro classes everyone takes. Then the average class size of the classes offered is quite small, but the average class size of the classes you take is quite large.