This is why I said the characteristics you were looking for are those more commonly found in small, private schools. After financial aid and scholarships (varies greatly from school to school, though), hardly anyone pays the "sticker price."
Smaller undergrad population = less people with the same interests (e.g., premeds) = more opportunities available per capita. Also, class sizes are smaller, with more support resources, chances to know mentors and professors, etc. The "price" comes with lots of benefits.
UTs are awesome, but [generally] fail where most other large-ass schools do in the above categories. It's all about what you value, which is hard to judge as a first-month freshman, hence my quip about only being in college for a month-plus. You don't know what the hell you're looking for yet.
WRT the research part specifically, students at private research institutions like my own typically start working in labs and other research gigs in freshman year, because there are enough spots for the small ugrad population to go around. At large schools like the UTs, I wouldn't be surprised to hear that PIs and grad students don't even begin to consider undergrads until their sophomore year when they have more coursework under their belt, which is pretty ridiculous because lab is 90% experience and very little background knowledge in science beforehand is needed to do a good job.
Take it from someone at a small Ivy (i.e., as opposed to Cornell with 10k+).
Too true. Luckily OP is transferring next year, so he should be able to somewhat gauge where he is.
