Just PM'd Atreidae....hopefully he will drag his head out of his arse....and be socialable. lol
Bugger you Ray, lol
Theres a few ways you could do this with an Arduino. the issue is really getting it all coded right and making sure you get a stepper with enough tourqe
The Arduino is a little computer that basically takes inputs, runs some code you write and does some cool output.
The buttons would literally tell the computer "he wants first now" and move the stepper to suit.
Stepper controllers from Polulu are easy to control from an arduino (want it to move 100 steps? send it 100 pulses)
Pololu - A4988 Stepper Motor Driver Carrier
Stepper motors however have No Idea where they are, if they stepped or if they are jammed (remember those grinding noises in cheap printers as the head slammed home.. yeah that)
So you need to make sure your stepper arrangement can push/pull the leaver under all load, AND! just for completeness needs a microswitch or similar to determine when its "home" (probably park), thankfully the Transmission should be able to provide that.
Servo's on the other hand have feedback circuitry in them that lets them know "where" they are.. even if moved by an external force they will return. but have far less torque
If you want to get started down this deep and dark road I can help you.. But it seems to be a complicated way of solving something that should be simpler to fix mechanically. (I'm sure you have your reasons)