What kind of yarn is best used for size 3mm crochet hook?

A 3mm aluminum hook (in the U.S.) would probably be a C hook. (Hook sizes are not always the same when made by different manufacturers.) Fingering or sock yarn would be best suited to this size hook. That said, manufacturers generally note the suggested hook size on the label of the yarn. That is a suggested size only and you are free to choose a different size hook with which to work that yarn. Also, your pattern will likely tell you what size hook to use and the appropriate yarn for your project.

If you are looking at steel hooks, you would have a size between a 1 and 0 hook which would be used for thread, probably size 5.