Pompeii has its own free luggage checking, and while I did not use it, no one posting here has ever had any trouble with it.
There is a sheet of fixed taxi rates you can download for Naples. Although it says (in Italian) that all fixed rates include "all extras", southern Italy can be a bit ... lawless. So print out the sheet to wave at the driver.
Note that this is a long and expensive ride. What are your plans after seeing Pompeii? You can't rely on finding cabs sitting around there. Can you take your luggage on the crowded commuter train to ?? ... Sorrento?
Edit: Maybe you are arriving so late you want to cram Pompeii in before sunset? Be sure of their shoulder-season hours and last admission time. Why not go to the hotel and visit Pompeii another day on the really cheap commuter train, free of luggage?