As ab intro to competition shooting think about the Umarex Boys Club. No fees and plenty of competitions to have a go at - both pistol and rifle. You just print out the targets you need then submit scores by e-mail. Shooting is at 6 yds and 10M.
A great way to get into something a bit more serious than garden plinking and at low cost too.
http://www.umarexboysclub.co.uk/