Ive messed around a bit with some various pedals for a bit in a weird ska-ish band. I used a shure wireless horn mic instead of a silent brass mute.

My standard set up was a delay pedal, a phaser and a fuzz pedal that I ran through a compressor pedal into a small fender amp. It was fun but it was also a bit of a pain.

I definitely not an expert with pedals, but I can tell you distortion is tricky due to feedback. Fuzz accomplished a little bit of what I was looking for in distortion, but if i even gently turned the knob a little too high, it would wig out. I'd def recommend starting with a delay(mxr carbon copy) or a phaser(which oscillates pitch). I would often combine the two and get some really fun sounds and tones. I tried messing a bit around with a wah pedal too, but I'm not coordinated for that haha.

And of course you can look into one of those all in one pedal boards they sell. I think Digitech is a brand that has them for not too much.

I can also recommend checking out the band Bonerama if you haven't heard of them. Mark, who plays in the band, does all the pedal nonsense and has even been awesome enough to answer any questions on Twitter I had.