In Norfolk or for that matter anywhere in the UK, you will need to wear a wetsuit. The water is cold. In the height of summer you may be able to get away without one, but you won't last very long in the water, so you're better off with one.
If you look on beachwizard.com and look under England > Norfolk, you will find a few breaks in your area. I've heard East Runton is supposed to be good.
Before you go rushing out to buy loads of kit, I would advise that you find somewhere that hires out boards and suits. Check out some of the local area to see if there are any surf shops! See if you can get your parents to take you either the West Coast (Cornwall/ Devon/ Wales) where surfing is bigger business and there are more hire locations. Failing that, there's Brighton or Bournemouth which are probably closer.
Rent yourself a wetsuit and a foam board and give it a go. If you make it over to the west coast, it may be worth having a lesson so that you get to surf with a bunch of people.
At 14, surfing is quite an expensive sport to get into - a wetsuit will cost you about £150 (around £80 second hand) but DON'T buy one without trying it on first - it should fit tight just about everywhere!
Second hand boards start at around £150 for a battered old one. To get a good quality second hand mini-mal (the better board for beginners) you are looking around £220 +.
That said, I started surfing at 16 and my first lot of kit lasted me 5 years! Look around at some online surf shops - some of them to 'starter kits' with wetsuits, boards etc all in.
If you need more advice about boards or wetsuits, post them here and I'll get back to you!