I doubt an Arduino has the processing power to do much if any distortion on a sound. You're probably better off using ready made distortion devices.
For the breadboard: you're talking solderless? Those are fantastic for development on your desk, but worthless for just about anything else as stuff will fall out and so. Get a protoboard aka perfboard to solder your final circuit on to. That will make it much more stable, and no risk of wires falling out. You can add some headers to plug a Pro Micro in to, or go completely bare bones at that stage and get an ATMega328 chip (they come in DIP package).
Protoboard looks like this:
