I posted some of this in the Republic of TX thread, but it's worth repeating:
There are a lot of parking garages/lots in the medical center, but the monthly rates are quite expensive. I believe the cheapest ones are $60/month. Some students that commute in my class find random places to park like near some apartments such as Lanesborough, and then they ride the rail from there. I've also heard of some people parking near the zoo, but I don't exactly know where. I also know of some students that park in large parking lots such as the ones in front of grocery stores, and then take one of the Metro buses to school.
I don't drive to school, but as far as I know, there aren't any special monthly deals for UTH students. Someone please correct me if I'm wrong.
You do get discounts for the Metro rail and buses. The normal one-way fair is $1.25 but as a student, you pay $0.60.
There's the student shuttle, which is free to ride (well, it's part of our tuition...) but you have to live along the route. Or, you could be sneaky, find a random parking space nearby, and then hop onto the shuttle.
The bottom line is that you really, really don't want to pay for parking unless you absolutely have no other choice. That money is best saved for other things, like a good drink.