which battery for generator 65-69 Big Twin / 65-81er Sporty

Tach, would like to convert my old Flatty to 12V. Have a Lima + controller with the data 65-69 Big Twin / 65-81 Sporty. Should probably be for 32Ah battery. How big does the capacity of my battery have to be at least, so that I don’t get overcharging problems? Wouldn’t want to install a low charge controller as much as possible. Danke schonmal für helpfule Antworten. I.B.