It's hard to estimate what sized battery you want. A deep cycle battery is a definite want, as you aren't looking for high current draw, just long runtime. As for the charger, there are many good RV and Marine battery chargers that would do what you are asking for, regardless of what sized battery you end up purchasing.
For battery sizing estimation, you are looking at about 50 to 55 amps (@ 12Volts) with that setup, which means you'd be looking at less than 2 hours runtime with that 100 Ah battery.



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