I'm not sure, but a servo doesn't sound like the right thing... A servo is an "angle motor" (typically about 270 degrees of rotation). You could rotate a plectrum with it, but it's probably not what you want.
One advantage of servos is that they have the driver circuit built-in so you just supply power and a control-signal from the Arduino.
Multiple [u]solenoids[/u]
might work but without some kind of lifting mechanism it's going to pluck the string again when the solenoid returns back to it's neutral position. I sort-of think you need a lifting-mechanism no matter what you do unless you want to "hammer" the strings like a piano.
A stepper motor with a pulley might be another option. Like a servo, you can move a stepper a certain distance and it can be reversed, but it can turn 360 degrees and make multiple revolutions. (With a stepper you have to find your "home" position before you start stepping.)
A regular DC motor can turn in either direction, but if you want to stop it at a certain point you need some sort of sensor.