Thanks for clearing up some things, Robin2!
Robin2:
The motors that @Zoomkat referenced (which are widely available) have 64:1 gearing so that means 64 x 64 steps (3840) steps per revolution
I'm not sure I understand. Does this mean that I can control the motor so fine that in theory I can tell it to turn 1/3840 of a revolution or (360/3840 =) 0.09375 degrees? This is a very fine control.
Robin2:
You could (perhaps should) add reduction gears to the small motors I suggested.
Do you mean to turn the slow turning of the motor into a faster turning of the wheels? I am not sure about this idea because this means more hardware parts which have to be screwed at the right places to connect properly. (Still a bit shy to add complexity because I don't have experience with robots.)