Newbie needs advice on simple project

You should describe how you wired up the buttons and attach your code. The servos are slow (how slow in terms of rev/s?) because they are probably running a gearbox to slow them down. What kind of speed are you requiring for the rotation? You could use solenoids or compressed air for faster action. After all, guns run on compressed air, right? (I assume you are trying to make a turret of some sort?!)