Yes, I would not recommend a 12A, constant 13.8V charger. 25A, 3 stage would be a minimum, but adequate, choice.
It depends on your definition of damage
Buy bog standard "leisure" lead acid batteries, and run them down each time until the lights go out, and their life will be considerably curtailed, especially if you don't fully recharge them immediately.
Run the same ones down to 50% of their capacity each time, and their life will be as good as they can be (notwithstanding other forms of battery abuse!).
Buy expensive traction batteries and they will be FAR more robust to running flat.
Which is why I'm a fan of battery monitors as they take out the guesswork and give you a remaining capacity gauge, akin to gauges for diesel, fresh water, waste water, etc.