This is straight from memory, so someone correct me if I'm wrong.
Polyester is the best for lead ropes. It's won't rope burn you, it won't get fuzzy, and it won't collect debris. It's probably the most expensive though.
I don't think Polypropylene or Nylon are prone to rope burns either, but they definitely will fuzz up. Not too bad at collecting debris. I like polypropylene for daily use because they're cheap and when they get fuzzy, you can just buy a new one (and that means new color!)
Cotton - yep, rope burns, and all sorts of shavings/debris/burrs/small animals will get attached to your rope.
Monte - 15 year old Paint/TB
Auric - 13 year old Arab