There is a formula to figure how much trolling motor thrust you need.
Loaded boat weight / 100 * 2 = thrust
Example: 2,200 / 100 * 2 = 44 pounds of thrust.

I like to add a little for excess wind.
Loaded boat weight / 100 * 2.5 = thrust. Gives a good fudge factor for wind.
2,200 / 100 * 2.5 = 55 pounds of thrust. So a 55 pound thrust trolling motor would be sufficient.

Definition of Loaded boat weight = Boat, plus passengers, plus boat motor + gas, batteries, trolling motor, fishing gear, anchors, etc. Everything on the boat.

As for batteries. With a 12volt Trolling motor you can start with one battery and see if it meets your needs. If not, you can add another in parallel. I would also start out with group 31 batteries. They are heavier, but will hold a charge longer.
As for hauling the batteries, get a cart, dolly, wagon. Bigger the wheels the easier it will roll on rough terrain.
Solar panels would be a great option if your not using the boat everyday all day.