12v 7/9AH form factor LiFePo4 are pretty popular now, they have efficient C rating of 1 which means you will get a longer runtime and last years if not a decade. They have integrated BMS to handle 12V lead acid chargers.
They do have a lower current limit though.
Lead acid are efficient at 0.1C so pulling 9A from 9AH above 10.5V will only last around 30 mins, ~ 1 hour for Lithium, your hardware will pull around 15A assuming its dual battery.
Peukert's law
