mAh is a measure of capacity.
If you want to drive all 18 servos at peak current, you need a battery that will supply 2.7Amps.
LiPOs tend to rate their discharge capability in terms of C, which relates the capacity to the discharge rate. A 5C battery is rated to be able to deliver 5 times its rated capacity. If you used a 5C battery, you would need a capacity of only 540mAh, though more than this would be entirely acceptable, and preferable.
You have a choice of two cells and dropping the voltage with a buck converter, or a single cell and raising it with a boost converter. Both types of converter are readily available. The buck converter would use a lower input current, though that doesn't matter much at this power level.
Don't forget that going through a buck or boost converter will change the current drawn.
With a single cell design, you will not need a charge balancer. Do be aware that you will need a specialist charger for LiPOs, they are easy to damage through overcharging.
With a 2 cell battery, it will be possible to use a separate linear regulator as well, as an auxiliary low current output perhaps for your controller.
Many servos that I have seen have a wide enough input voltage tolerance to run from 6v, which would allow a 6v SLA for the servos and a LDO for 5v for the MCU, though not the sg90 I notice which specifies 4.8/5v. Perhaps these are anticipating a 4 pack of NimH (nominal 4.8v)?