Assuming you're going down on one of the club weekends where they set up a winch?
Trainers would be fine, I think you can basically wear what you want but personally I'd avoid jeans because they won't be that comfortable to walk up in and if they get wet they'll be nasty to wear.
I think bringing waterproof jacket and trousers is a good idea too (there are still some drips when you go down even though the stream gets diverted), although I think last time I went they had some that you could borrow.