As far as battery tech goes, you can get extremely expensive batteries (Lithium\Gel\AGM, etc.) or cheaper ones.
But, the good ones you would need would be considered Deep Cycle for Marine applications or Solar application even better. They can be discharged further and provide a more even discharge curve.
They are measured in Amp Hours rather than cranking amps. 1 Amp Hour is just what it says. Lasts for 1 hour on a 1 Amp draw. 100 Ah = 100 hours @ 1 Amp or 20 hours @ 5 Amps.
The V3 Draws about 1.12 amps @ 5.1V DC (5.712 watts). So the first thing you will need is something with a simple converter already built in. They sell a cord with alligator clips on one end for the battery connection and a 12V cig lighter receptacle on the other. Then use a 5V USB cig lighter adapter like you would for charging your phone. Preferably one without a LED light that will draw power. That will at least get you experimenting with what you have. It will probably mean regular charging though if you don’t add a charge controller and solar.
So, the higher the Amp Hour (Ah) rating on the battery, the longer it will last before needing to be recharged. Each battery brand\type will only recommend 50% to 80% discharge before recharging depending on the quality. The % you discharge will affect the life of the battery. The deeper you discharge it, the more it takes from the number of charge cycles it can withstand in it’s life cycle. Good batteries will publish the data and graphs to show where the discharge sweet spot is for max battery life.
There are many calculation pages online to help you calculate the number of hours your ? Ah 12V battery will run w\ a 1.12 amp @ 5.1V DC (5.712 Watt) draw down to ?% before a full recharge.
UPDATE EDIT: Theoretical numbers here in a theoretically perfect world:
If you bought a high quality purpose built 100Ah 12v deep cycle battery, 100Ah x 12V= 1200Wh… @ 85 % discharge = 1020Wh delivered… @ 5.712W = 178.57 hours service. About a week. If you have a 50% discharge life cycle sweet spot = 105 hours to get the longest life from the battery. With a charge controller, this can all be automated to extend the life of the battery.
A 100Ah 12V AGM will run about $200. Double that for a Lithium.
Good luck!