You seem to be trying to digest a lot of info for day three of your guitar playing. I don't know that you need to be thinging about
CAGED just yet. But here here's my stab at explaining:
For your I-IV-V example in G, The key is G so you only have one sharp F#. The chord tones are GBD for G chord, CEG for C chord, and DF# A for D chord so all your chord tones are in the key of G.
The CAGED system only deals with chord shapes. As these shapes are moved up the fretboard the actual notes change as the form moves. For example you can play the G chord using the (E) form if you place the form at the 3rd fret, the notes of the chord would still be GBD. If you
slide this (E) form up one fret you are playing an Ab chord with notes Ab C Eb. etc.
One way to apply the the CAGED with the I IV V would be to play the (E) form at the third fret (G chord), then the (A) form at the 3rd fret (C chord) and then the (A) form now on the 5 fret (D chord). In another example you could play the (D) form at the 5th fret (G chord), the (A) form at the 3rd fret (C chord), and then the (C) form at the 2nd fret (D chord). Keep applying approach and you end up being able to play I IV V in any key anywhere on the neck of the guitar.
Hope this helps,
Robert