Your charger is 200W, lets assume it is running all day long (8 hours), that is 1600 Watt-hours, divided by the 12V from the supply gives you 130Ah battery capacity (roughly).
Now I doubt you will be using the charger at its limit ALL day long - I'll wager that a 100Ah battery in good condition would be enough.
If you are buying a battery, I'd buy a deep-cycle. If you have acquired a battery for nothing, then give it a try!
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