I actually used 5/16" rod but located where it is under the table the slot minimises the runout of the rod. Since you plan to mount the drive rod on top I think 3/8" might be the best compromise. Easier to hide. I thought I was going to have to attach the drive to at least two wheels but was pleasantly surprised that it ran true without crabbing using a single wheel. It takes little effort to move the crane so a simple screw attachment of the nut to a leg will suffice. I did replace the diecast wheels on mine with sintered wheels from a Post War 2046 Hudson engine truck. The repro parts guys sell these and they are the same size as the die cast ones.
On my first version I supported the drive rod with ball bearings on both ends. The version shown only has the bearing on one and the other supported by the motor itself.
Pete