You can put whatever battery you like on, unless your using a motor Mover or going off grid then use a 110amp or more. Always periodically use a bench charger as the caravan charger is only a trickle charge.
When going off grid, then you do tend to need the biggest battery you can fit, but caravan movers are not the battery killers some people suggest.
I have done several quick calculations over the years and it shows the amount of battery charge they are likely to use is surprising small typically amounting to less than 2Ah to position and set up or store a caravan. That is not a lot in the grand scheme of things. By comparison using a 24W TV for a couple of hours will use twice the energy of the mover. If moving is all you need a 12V battery for then a cheap car battery is more than enough provided it can be recharged and kept topped up.
But the problem can be with leisure batteries, they are normally used for situations where a long slow and deep discharge might arise, and their design limits the peak or cranking currents they can deliver. Some caravan movers need a battery with 80 to 100 Amp peak discharge capacity and that might unduly stress some smaller or less well made leisure batteries.