You're looking for the right servo and/or the right servo controller? For the servo controller, you can get away with something really small like the 08M Servo Driver
(you'll also need the download cable
). This allows you to control three channels (for in your case, channel 1 would control servos 1, 4 and 7; channel 2 would control servos 2, 5, 8; channel 3 would control servos 3, 6, 9). You can operate the servos in both directions. You would connect it to a push button for example (one click one direction, second click reverse, third click to stop.. it's up to you to program it to do what you want). For the servos
, you'd need ones which are powerful enough to move the load; you might even choose three servos instead of 9 and use mechanical linkages.