Different hair types and different styles call for different tools. Here a few you may need:
Hard plastic or metal bristle brush
These are good for getting the tangles out of thick hair and moving a lot of hair into a style like a pony tail. The kind that are squishy in the middle don't hurt as much since the bristles are more free to move when they catch on a snag.
Soft bristle brush
The soft bristles smooth the top layer of hair to "fine tune" a style. These brushes work for finer thin hair to get tangles out, but won't do the job for thicker hair.
Wide tooth comb or pick
These are good for combing through wet hair. Use these when you want to undo a braid or twist and keep the curl or wave without making it all go poofy or frizzy. Also if the hair is very curly, a regular brush may cause a big frizz, so a wide tooth comb or pick can be use to get the snags out.
Fine tooth comb/rat-tail comb
This is the best tool for parting hair. It can also be used for styling short hair, ie. boys' haircuts. A rat-tail comb is named after the long thin handle that looks like a rat's tail. It is good for making zigzag parts. I am sure there are plenty of other types of brushes and combs that are useful, but these are what I have, and they will do for the scope of this blog.