I agree with @Greenonline 's recommendation regarding LiPo batteries along with his warnings on battery care. It seems you will need a fairly small battery, considering your current requirements (about a 1000-2000mAh 2S LiPo).
However, you also need to add 2 5V BECs (5V regulators in RC lingo) to power your circuits; The 7.4 or 11.1V provided by the battery isn't very useful.
You can find more on BECs on @Greenonline's link. Especially the youtube channel RCModelReviews provides good info.
I suggest having 2 BEC to avoid servo noise on the RPi power rail, as you mentioned. Servos and motors apply intermittent loads on power supplies. Most of the time (especially on cheap power supplies), this causes severe voltage ripples on the power supply line. If sensitive (from a power supply point of view) microcontrollers or ratiometric sensors are to be used in the system, it's best to attach them on a separate regulator and leave the battery to act as a "buffer" from the servo ripples
I'm not familiar with e-bay sellers, but something like this would be adequate. If you prefer paying an extra buck than taking chances with Chinese products (I do take chances usually), you can also look at this product.