In reply to Francescos:
Hi
Is it too soon to start climbing outdoors - No I would recommend starting as soon as possible. Starting indoors is like learning to play football by going to a club's training sessions and dribbling round cones before you have your first kick-around in the park.
Grades - the V grade in London walls is so debased as to have become utterly meaningless just ignore it.
I'd suggest the peak district as a destination.
The same shoes should be fine but a good scrub under a tap to get the chalk off will help and take something to clean shoes between goes - and use it.
Post edited at 14:45