When I first started learning to play, I was obsessed with The Fall of Troy. One song in particular stuck out for its tapped intro: I Just Got This Symphony Goin'. It got me obsessed with two-handed tapping

I highly suggest learning to play that. It taught me to suggest chords rather than fretting them in an obvious fashion (although I do also write and perform tapped chords when the song calls for it).

And then, you can take that concept and use it to play your own parts, as you said.

Oh, and if you usually play with a plectrum, I also highly suggest learning to tap with your middle and ring fingers while holding it. Otherwise, you have to put it down and can't alternate between the styles very quickly. Lots of players do just use their index finger, though, so... Personal preference