What kind of battery source do I need?
I'd recommend a 3S LiPo battery pack. These are commonly used in RC vehicles, drones, and robotics.

These batteries are nominally 12V and can provide current far in excess of your application. They're also inexpensive and easy to source.

One consideration is that these batteries are damaged if they're drained too far. You'll need to add a UVLO (undervoltage lockout) and voltmeter to your project to prevent permanent damage.