I can't think of any situation in which the 1-2-3 fingering would be preferable. Definitely, use the nephew's 2-3-4 fingering. Grab has a point about the weak little finger. I suspect the beginner's books reference the 1-2-3 fingering because they think it's simpler for the beginner to learn; never mind that it's not really useful.

As far as learing all possible G chords goes, every moveable chord shape becomes some variant of a G chord at some position on the fingerboard. Learn all the chord shapes you can and play around with them as you learn your way around the fingerboard.

      - Mark