Wallace and Hobbs is definitely the go-to for most freshman and sophomore-level meteorology classes.
Even had a few upper-level courses that referenced it. Maybe a bit more advanced for what you're looking for, but still is an excellent textbook. Still have mine in my office.
The standard intro to atmospheric science I believe is Wallace & Hobbs; this book focused on the physical science and quantitative aspect of atmospheric science. I don't have anything for general geophysics however.
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I once heard from a guy having a physics PhD now working in weather forecasting said "Even the most theoretical ideas in meteorology is nowhere as sophisticated as in theoretical physics." Atmospheric science is more of an applied science much like engineering. So I think all the really high-level theoretical tools in GR, QFT, etc. will unlikely be used there, and I suspect this is the same for geophysics as well. The more immediately applicable background knowledge to have, I would say, is fluid dynamics.
You'll be hard-pressed to find a better introductory textbook than Wallace & Hobbs. It's a comprehensive and informative introductory tome that still manages to have lots of judiciously chosen pretty pictures.
I personally prefer learning from books. Some of my favorite intro textbooks are:
The older editions of these books are perfectly good and can be quite cheap. (Whereas the newest editions are quite expensive.)