There are two things the motor needs to be able to do. Firstly provide enough starting torque to overcome static friction in the bearings and accelerate the ball up to the required speed in a reasonable amount of time. Secondly to be able to provide enough torque to maintain the desired speed against the friction in the bearings for however long you want to run it for.
Bear in mind that not all motors are rated for continuous running, this really comes down to how well cooled they are.
Equally on of the big determining factors will be how good the bearings are and how well balanced the whole thing is. For a target speed of 1rpm you will need a fairly substantial reduction ratio gearbox anyway.
I suspect that the most convenient solution will be a DC motor with an integrated planetary gearbox as these are an off the shelf solution to high torque low speed applications. At a very rough guess I would say you are looking at something in the couple of hundred watt range.
You might also want to look as something like the hub and stub axle from a small trailer for the bearing as these are again a cheap and ready made solution.