Can someone explain the different types of .22 ammo for me please?

If you live in the UK you would not get a licence for that application. You may get one for a small bore shot gun (say 410) but not for a .22 and you would need to show that you were competent to use and store the gun safely - normally that means joining a club. You may like to look at .22 air guns instead they are adequate for your purpose.