Definitely not a stupid question! Applying to vet school is weird because the vet schools don't seem to have a set "standard" as to what they expect of their applicants...
One thing I would suggest doing is contacting the schools themselves about this, and how important the ranking of the undergraduate institution is. For example, I know that VMRCVM doesn't care what "tier" school you attended and won't give much preference to those who went to more competitive schools, where as somewhere like UPenn highly takes a school's academic reputation into consideration when accepting students.
Aside from that, not all private schools are better than all state schools. Just as an example, UVA is state school and is FANTASTIC (they rejected me back in the day... lame!), and is a better school than where I currently go, even though I attend a private institution now. Private schools also tend to cost an arm and a leg, so if monetary resources is an important consideration (which I remember you mentioning in other posts), then unless you can score some nice financial aid and/or scholarships, a state school would make more sense since it would be much cheaper, and would still provide a good education.
I also wouldn't necessarily suggest overloading in course work either, unless your plan is to graduate faster. If pre-reqs have been tough for you so far (and to be honest, I don't think they're easy for most... I hated chemistry ugh!), then focusing on just a normal work load and getting As and Bs rather than overloading and getting Bs and Cs (and Ds!) would be a better use of your time.
But yeah, overall... contact some schools you think you might be interested in. If you don't have much of a preference for which vet school you might eventually attend, then you could find out which schools place less of an emphasis on undergraduate school tier. This doesn't make the school any worse of a vet school, but it might help you get in and narrow down your search a little.