trustybutler:
So if I split the 12v supply between the LED strip and the servo at the same time, will the LED's brightness not be affected?
As long as the supply can provide enough power, no. So get a big enough power supply.
For your 6V servo best to get a buck converter rather than a linear regulator (you'll need a good heat sink as the regulators will have to absorb as much power as the servos take). Or you can get 12V servos of course.