I'm thinking it's going to be difficult to translate the short movement of a solenoid into the kind of "swing" or "snap" that a real drummer puts into a drum-hit. If you just wanted to hit the drum head with the solenoid armature, that might work.
I think a good sized motor with a gear, operating some sort of swing-arm, would be best. With a big enough motor, you could probably connect directly to the shaft without any gearing. I don't think you need a servo, because you don't need to precisely control position. With a regular DC motor, you can control the power/speed of the hit. If you want to move the arm/stick between different drums & cymbals, servos would be good for that.
Or a pneumatic or hydraulic cylinder, which can give you a longer stroke than a solenoid. (But, that requires a hydraulic pump or air compressor.)