That’s a hard question to answer. There are many good hard hats on the market, personally I like the Petzl Alveo Vent, but have friends who wear Kask or Protos hats.
My best recommendation is to choose one, approved by ANSI for the type of work you do, and within your budget. If you’re not sure which one to pick, go to an arborist supply and ask the staff for help, or call one the Gap Arborist Supply has a good staff that can help you for sure.
Another suggestion which will help us to never use your saw above chest level. That will greatly reduce the likelihood of your hitting yourself in the head with a saw, and reduces the chances of a limb hitting you in the head or chest as well.