Your RG370 is H-S-H, right?
For Greenday, a Seymour Duncan Custom or JB or Invader in the bridge position would be fine.
For blues, you'll want something milder with a strat sound, so a Seymour Duncan Duckbucker in the middle position.
The neck, maybe something like a Seymour Duncan Custom or Custom Custom or a Jazz.
My 2 cents.