Falchion:
I just need to obtain a battery that can support all of these servo motors.
Yep, and there's a lot of discussion about power supply on this forum!
I've just (literally yesterday) been given a 650W ATX PSU and using an Instructable like this we're converting that to a lab supply. The servos I have are happy at 5v, and I can also use the 5v to supply Uno through the USB. (Alternatively I might regulate that up to 7.x V with one of these (which I have) and feed that to the barrel or Vin).