[MrForbes]

You need to figure out how much current it draws, and how long you want to run it, then look up the datasheets for some batteries and see what you really need. They have charts which show voltage as a function of time and current load.

Also consider how the thing is housed and how much abuse it will take, and how safe it needs to be. Might be able to get away with a low cost riding mower battery?