Are you sure it's charging when running? a weak battery getting sent with the sold tractor would be expected also.
You can put any battery in there that will fit and reach the cables, 12V and hooked up correctly of course. I suggest a group 31 700-750CCA battery from your local heavy duty truck dealer, sometimes they go on sale and are the best value in batteries, since you're in PA, Deka sells blem batteries also if you get there.
You can get something 800-1000CCA at Walmart, but it will be thinner plates and less robust than the group 31 fleet battery. If your cables or clamps are questionable, I replace them with the screw top terminals, studs not post batteries.