Pro tip to anyone going to university (or has kids going to university). Find a low ranked state school that has a high teacher to student ratio. Also look at the percentage of classes with under 20 students.
I did my undergrad at one of those places. Currently the ratio is 1:17. The percentage of classes with under 20 students is 60%.
Because it's low ranked, the pressure to get grants isn't as high. Because each course has fewer students, the professors are much more available. As an example, a professor who had only 3 hours a week for office hours was thought of as "stingy". Most had about 6 hours. They'd combine the OH for all the courses they were teaching, and could easily offer 5+ hours because there are so few students (at times no one would show up).
Only one humanities course was taught by a non-faculty member. Everyone else was tenured, on the tenure track, or a permanent assistant professor (i.e. spousal hire).
The quality of education was pretty good, too. They probably had a lighter load than a top university, but I'm not sure that's bad. I went to a top 3 school for graduate studies, and took some of their undergrad courses while there. It was brutal, and the undergrads were clearly overworked. Worse - most of the work was just busy work. They weren't really working on anything more challenging than the folks in low ranked universities.
Down side: Your peers aren't as smart, and your peers are really what push you to work on interesting projects.
If you really want the name recognition, go do a quick MS at a top school thereafter.