That's what I was gettin at with C, D and G. They are simple to learn and great exercises. Once you can change between all three chords quickly, you've accomplished something.
a simple search of Doc Watson will validate this completely. He was a master at playing within the chord structure and pulling leads at the same time. His favorite key was C, which is also the same shape as F and G, and really the foundation chord that lends itself to the most diversity in lead playing.
my suggestion to beginners is simple, learn to play one song, front to back, singing and all. If you just learn the intros or signature licks of songs, you will be stuck in the world of noodling. I know a ton of good guitar players that can do the Crazy Train lick, but can’t play any of the rest of the song. When someone says….”hey, you play the guitar, play me a song”, you can play them a song, then hand the guitar back and say…..”now, play ME a song”!