Way to go, Stefan. Now to answer your question, while being practical:
Somebody did some research and found that in thirty million songs, one-third of them are written in the four major keys of G, C, D, and A. The most common keys of songs written in minor keys are Am, Em, and Bm. It’s noted that Am is the relative minor of C, Em is the relative minor of G, and Bm is the relative minor of D. Also E#m is the relative minor of A, one of the four common keys. Add to this the fact that G is the most easy key to play on guitar.
If you consider that guitarists often accompany piano, the key of C is the most common key for a piano, but not so much for a guitar. E is easy to play on guitar, but not piano. The key of G is easy to play on both piano and guitar.
What does all this mean? If you memorize the keys of G, C, D, A, Am, Em, Bm, and E#m, you’ll probably be able to play just about any song solo or accompany a piano player. And memorizing eight keys is much easier than putting the entire Circle of Fifths to memory. It’s a practical answer to your question. And let's not forget that wonderful thing called a Capo. Lotsa luck. Best, John