You’re a Texas resident? You’re not going to qualify for need-based aid? Then both Texas A and M and all the UT schools are cheap for you. And BTW, Texas has something like FIVE fine public medical schools, with the cheapest in-state tuition in the country, I believe. If you can get into one of them, you’d be smart to go there.
UT Austin is the flagship state U. If you can get in, go there. There’s a medical school, so there will be research opportunities. Austin is a bigger town than College Station. UT Austin is the most selective public U in Texas. It’s the obvious choice. If you’re afraid that you cannot hack the competition at UT Austin in the premed classes, you’re unlikely to do well in them at Texas A and M either. Forget Rice, Case Western, and Penn. First of all, they are hard to get into (like REALLY hard). Secondly, if you’re afraid of the competition at UT Austin, it will be much, much more competitive at Penn, Rice, and probably CWRU. Most importantly, the tuition will be literally 45K more/yr at the private schools, an extra 180K at least, and with you talking about medical school, you really need to keep your college costs as low as possible.
Third thing - tons of people who start out as pre-med wind up changing their minds along the way. UT Austin is going to have a LOT of really good departments and majors, since it’s the flagship.
You should look at all the state U’s in Texas, but if you can get in there, UT Austin is probably your best bet. It DOES matter what undergrad school you’re coming from. All other things being equal, med schools are going to take a person with a high GPA from UT Austin over someone with a high GPA from U North Texas.
So, yes, your father is right in that you should choose a public Texas university over those private schools, unless you would qualify for need-based aid. But you should choose the most competitive one that you can get into, and if you’re not in the ballpark for UT Austin in-state, you’re not in the running for Case Western, Rice, or Penn. Consider yourself lucky. If they’d had a better teacher for my kid’s instrument at UT Austin, I would have been pressuring him to go there, transfer his residence, and go to med school eventually in Texas. It’s a fantastic deal, in-state.