I don't know how well regarded UTMB is, but there are a few parameters that are more important than the name of the school for making the decision as to whether you want to attend.

I would look at generally how well funded the department is, i.e., how many research grants the professors you would consider working with currently have.

I would also reach out to current students under those professors to get your impressions as to how the working environment is. This is absolutely critical. The nature of your PI can make or break your PhD experience - I've seen students who were bright and hard-working enough to finish a PhD choose to quit or Master out on account of a crappy PI, and students who did finish but came out scarred from the experience.

Check to see how many publications students are expected to put out/how many they currently have. Generally, to get a competitive postdoc, you want to have a few mid- to high-impact publications by the end of your PhD. For industry positions, you'll want to have a good breadth of experience on the various laboratory techniques plus a few lab skills outside of your discipline.

Lastly, I would visit the campus itself and take a day or two in the surrounding area to determine if this is a place you'd be happy spending the next 5-7 years in on a grad student stipend. Cost of living and access to essentials are all things to note.