Probably on group 27 battery will be enough for your needs as will the 120 Watt solar panel. A good place to start is with buying a Trimetric charge controller so you can monitor accurately how much charge is coming out of your battery, how much charge actually remains, and how much charge is going back in when plugged into shore power or using the generator or the solar panel.
I prefer the solar panel approach as they keep the battery charged with nothing needing to be done by you and they will recharge the battery after a night's use automatically as well. No need to fire up the generator and stay to attend it. With solar once it is installed you can forget about it and let it operate.
One panel should be able to recharge your battery in 2-4 hours depending on the weather and time of year and amount of shade where the trailer is located. If you add a second battery that may change the charge time to 4-8 hours but that is still all that you need. You start the evening with the batteries at 100%.
