Arduino + Relay Explanation

The diagram looks good, and the discussion is fine so far. Just a couple of extra clarifications:

  1. I'm not sure that ALL solid state relays have a built-in resistor on the LED side. Check the datasheet to be sure.
  2. you can use a breadboard on the "control" side of a high-current relay circuit, just not on the high-current "controlled" side.
  3. MANY solid state relays will control AC only. Since that's what you want to do, you shouldn't have a problem, but you can't necessarily stick a 20A SSR into a circuit where you want to control 20A of DC current.