More important is the type of deep discharge battery.
Be sure to use an efficient inverter. Cost to run on batteries is highly dependent on efficiency.
Use a high quality CV/CC battery charger. See Charging Lead Acid
Is the pump running 100% of the time?
the generator does run around 6 hours a day so that should charge them
well and also give plenty of back up
Six hours may be insufficient to charge a fully discharged (50-80%) lead acid batteries. You will need at least 12 hours or use more batteries in parallel to reduce the depth of discharge (DoD). Lower DoD requires less charge time and gives you more charge cycles (longer life).
Shoot for a maximum 50% discharge. See How to Prolong Lead-acid Batteries
I would say two 100 Ah would be the minimum. Three or four may give you the needed charge time and longer overall lifespan. Budget $1000 per year.
For fastest charge time an Absorbent Glass Mat (AGM) would likely be best.
Example: Duracell Ultra 12V High Rate AGM Sealed Lead Acid Battery