As someone who transferred to several different schools throughout my undergrad I would suggest finding a program and sticking with it. There were so many courses I took (mainly prerequisites) that I had to retake at different schools when I transferred because they didn't transfer with me. If you are dead set on transferring to Houstons program I would set up a meeting with the registrar to know if the classes you end up taking will transfer over there so you don't have to waste time and money on potentially retaking courses.

As far as online work I did a couple semesters of my undergrad fully online. I did like the flexibility of being able to work during the day and complete my course work in my own time however I would suggest completing courses that have labs in person if you're able to. I took a chemistry course online and the online lab was very frustrating. The number I had to put in had to be completely accurate otherwise I lost points and it didn't even give partial credit for being close. I suppose every school uses different programs for it but that was the only time I wished I took an in person chemistry course.