Wait...think I figured this out. I didn't realize when I installed that Fantastico didn't have the latest version! I have been downloading 1.5 templates, when the installed version is not 1.5. How do I install 1.5 when Fantastico doesn't have it yet?
That's definitely the problem. My advice: stick with what's supported by Fantastico until you have more experience. I have 2 active and 2 test Joomla! sites and the 1.0 series does everything I need. There are lots of templates out there for the 1.0 series, just look closely at what you are downloading. Hope this helps.