Below is a list of common hook sizes for US and UK, including Metric sizes which are the ones commonly used in Australia and New Zealand. In this table you can find the hook sizes required for most projects from blankets and appliques to amigurumi (the japanese art of crocheting stuffed toys).
Hooks also come in very tiny sizes than you can only get in steel hooks, these are used in very small or fiddly projects to crochet with thread. Got your eye on crocheting some doilies? I admire your tenacity! Check out the next table for your hook sizes.
You can get many different hook types, most of which are interchangeable and depend on what you prefer. Metal, wood and plastic.
If you find yourself having hand or wrist troubles from crochet, any kind of aches and pains from gripping you can also get ergonomic crochet hooks. These have much large, shaped handles to help ease your grip a little. There is the perk that some of these hooks come in really beautiful designs