There are many crochet hooks to choose from, and it all mostly comes down to personal choice. I have said many times that I prefer to use a 4mm hook with 8ply yarn. the hook size and yarn thickness will determine the size of your finished item. It is always best to check the yarn label for the recommended size
I still use the same hook I started crocheting with, pictured above, a fairly unremarkable metal hook (4mm of course) But have a large collection of wood, metal and plastic hooks. I also sell hooks through my Etsy shop, so I've had a chance to test a few styles out. (Link in the right side bar if you want to have a look!)
I really like the feel of wooden hooks, like these bamboo hooks. You can get some really pretty wooden hooks, with turned handles. They may not improve your crocheting, but they may inspire you to use them more often! Check out these beauties on pinterest
When using finer hooks, or even if you are working for a long time, I find the hooks with a thicker grip are a bit easier on the hand!
If you are used to a certain style of hook, you might find changing the weight or grip takes some time to adjust.
As with most things crochet, depending on where you live in the world the hooks are going to have a different method of sizing. Below is a chart to compare, but you may find some brands may differ, and older vintage hooks may not match today's sizes. The metric measurement refers to the diameter of the hook shaft.