The ideal battery would be a "garden and tractor" battery: small, cheap(ish), and usually built to withstand a bit of idle time. Not a whole lot of reserve power, but you aren't going to be cranking the motor off it, so that shouldn't be too much of an issue.
On the idle time point, I meant time between running the motor (i.e. time between charging); I kept a small 200mA trickle charger on the battery for my Honda 40 when it was parked at home. I never really looked at the solar panel trickle chargers, but they would probably do, as well. So I never actually tested the shelf life of the charge.