Computer Controlled Large Slow Stepper Motor
I don't see the point to a stepper motor.  What you want is a ordinary motor greatly geared down.  The overall power shouldn't be that much since you say you can move this with a couple of fingers, and you only want to go around once in 1 to 3 minutes.

You probably don't need anything more than a DC motor and a variable bench supply you adjust to get the desired speed.  It doesn't sound like speed is critical, so a fixed set point determined from experimentation is probably good enough.  There are plenty of off the shelf DC motors and bench power supplies that can drive them.  It sounds like the actual power output is less than a watt, but you probably want a motor rated for a few watts.  Make sure the motor is OK with continuous operation in the regime you will be running it at.

The hard part will be to couple the motor shaft after significant down-gearing to this large rotating table, but that's a mechanical problem out of scope here.

If you really want to control the speed or know where the table is, then connect a shaft encoder and control things from a microcontroller.  Use a fixed DC power supply and a low side switch that is driven by PWM from the micro.  The micro would also receive the shaft encoder outputs to determine speed and position.