I just got a DVD+RW drive and I am a true newbie, I bought a pack of DVD-Rs and when I insert one to burn onto, the computer doesn’t recognize it at all, and says that I need to insert a disc. Are DVD-Rs not compatible at all?

Different standards and not compatible.
If your drive isn’t a dual format drive, you can only use one of those standards…

To learn more you can read in this forum, there are a few topics that explain the difference between DVD-RW and DVD+RW