The Mini Maestro is not necessary; the Servo library will handle 24 servos on the Mega with no external hardware. The Mini Maestro is fully compatible with the Mega, however.
You need to be more precise with your sensor requirements. "Touch" suggests a button would work fine, "light" suggests a phototransistor or photoresistor, and "motion" is much too vague to respond to.
For a battery I'd suggest the LiPo batteries commonly used with RC cars/planes/etc. You will also want to buy a hefty "BEC" or two which will regulate the voltage to 5 or 6V for your servos. The Mega can regulate the voltage on its own.
Arduino Mega prototyping shields are common an inexpensive on eBay or you can get generic prototyping boards. You'll also want to get some handfuls of male and female "pin headers". For wire I would suggest round telephone cable from the local hardware store, but depending on the amperage of your servos that might be just a bit too small of a gauge. Beyond that there's still a bunch of resistors you'll need to use with your buttons ... a guy could go on forever here.