In reply to tonygreenhalgh:
I assume you're going to continue with leading on a single rope outdoors rather than halves? If so, then I'd go with something thicker than the 9mm suggested above - rope resistance to abrasion and cutting is generally proportional to diameter, with fatter being better. I don't think I'd go bigger than 10mm now though, many modern belay devices struggle with 10.5s.
The question is, are you going to be climbing with people that already have ropes? if so, you're better off spending you money on something else at present.