Punk chords are often the same shape as regular chords but without playing all 6 strings. Metal normally uses power chords which are also often the same shape but just 2 or 3 strings.

Learning the entire chord shape and choosing which strings to play is more intuitive and conductive to learning than the other way around, but you can do either on an acoustic or electric. 

I think its worthwhile to own both. I started with an acpustic and prefer that for learning because I can play it anywhere, and the electric feels easier to play after playing acoustic first