I searched around and couldn't have a straight answer. Complete beginner but I'm doing ok on the CAGED system so far. I've memorized where to put my fingers for EAD and feel pretty comfortable so far. Right now I'm working on switching between them with enough speed and cleanly. I know I still need to work on C and G but after that where to next? I've see post that suggest scales but I'm not too sure. I won't move on from CAGED until I feel comfortable with the whole thing but this is really to set a goal for myself.
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I would say barre chords?

If not that then maybe try the first position pentatonic scale.
if you have the finger strength then bar chords if not scales or you can go the theory way and learn key signatures an memorize the notes on the fret board and make ur own way of playing the scales witch will ultimately let u shred
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To be honest, the most fun way to learn is to find songs that you like, and learn how to play them, starting from the simple ones (ones which mainly use the E,G,A,C,D chords, in your case). Every now and again you'll come across new things in these songs and you'll expand your knowledge that way

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