If your air temps are steady at 78-85 I would unplug the uth until you get the stat.
Now as for the tub vs. tank issue. It really depends on you, your budget, and keeping style. I like naturalistic tanks so I still use two glass tanks. I also have pvc cages and a rack but I really do like the look of a glass tank. They are however more work to keep the numbers right.
Starting out I think a tub is a good choice and you can secure the lid with alligator clips, luggage straps, or bolts. They are cheap and easy to clean and replace so you can put more money into the tstat for now and worry about a nice display style cage later if that is your end goal.