The University of Minnesota-Morris comes to mind. It is not well known but it is a public alternative to the small liberal art school experience.
A. Small class sizes.
The biggest intro classes are capped at 75, most other classes have under 20.
B. Sufficient capacity exists so that the school can hold the line on small class sizes without shutting any student out of a class because it is too full.
I can’t really speak to this, but I would assume so.
C. All class sessions led by regular faculty, with minimal or no use of TAs or adjuncts.
No TA use, all classes taught by professors.
D. Good selection of majors, and good selection of course offerings in each major, including core junior/senior level courses for the major offered at least every year (preferably every semester if part of a sequence of prerequisites).
35 majors, as well as the opportunity to make your own.
E. Undergraduate research opportunities (which presumes that there is some research activity at the school).
Perhaps more opportunity for undergrads that at a big school–there are no grad students and a lot of research is done.
F. Low cost.
About $20k for all costs, for in and out of state students.
While Morris perhaps doesn’t fully meet every single requirement, it certainly comes close. I visited it recently and was pleasantly surprised at what I found.