What kind of micro servo would I need?

Jay98:
28BYJ48 Stepper Motor 5V - emartee.com

Would it work?

Those steppers aren't quite as precise as they should be (~4000 steps per revolution, but they tend to miss one or two each revolution). If you could add something to track your position once a revolution (optoreflector, hall effect) then you should have no problems using it for a clock.