Is “grade level summer precalc” an accelerated option for advanced students or a remedial class for students who struggled during the year? I’m sure you see how that’d affect the pace and rigor (it’s okay if the course is just an intro to precalculus rather than accelerated&advanced: since you won’t be taking any precalculus or calculus in college it doesn’t matter - most “math gen eds” like Math for Citizenship or Art&Geometry only have Geometry&Algebra2 as pre-reqs.) If you’re struggling in Algebra2, you do NOT want to take an advanced/accelerated precalculus class over the summer !
I would recommend AP Stats Sr year and APES for a science, however your remaining courses better be the most rigorous your school offers - 2 from AP lit, AP foreign language, AP Euro, AP Art History, etc. as well as Honors Humanities, Social science, and Art classes (at least 2 more from the above subjects).
For UHouston, make sure to apply as soon as the app opens and to Honors.
If you’re struggling in Math, not sure TAMU is the best choice.
Run the Net Price Calculator on Trinity, Southwestern, TCU, Hendrix, UNM, Texas State.