For all preparation methods (espresso, plunger, drip filter, stove top etc…) the only type of grinder that is adequate is a Burr Grinder. There are two types, flat burr and conical burr. Flat burr grinders are adequate for domestic and most commercial applications.
Do not be fooled by marketing! If you look into the top of a “coffee grinder” and see a silver propeller “blade” understand that you cannot grind with a blade. These “grinders” were originally marketed as spice grinders but with the popularity of coffee have been renamed and marketed as “coffee Grinders”. Although they will break up coffee beans, particle size will be inconsistent and therefore, inadequate for espresso and frustrating for other approaches.