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For the wheel I would spend some time making a shouldered arbour to hold the blank and turn between centres. This will allow the part to be machined on both sides if required and also allow it to be put in a repeatable position each time the part is mounted in the lathe. If you don't want to work on both sides then an arbor with a shoulder and expanding centre will allow repeatable positioning as will soft jaws cut to grip on the inside of the bore. The soft jaw option would also allow the axles to be machined at one end using a collet or plain bore soft jaws. Then re-cut the soft jaws with a lip to position the already machined end in a repeatable location. Alternatively I would use a collet in the spindle holding a? piece of bar to act as a fixed stop and soft jaws to hold the axle in a known position. If you have 5C collets then a suitable back stop can be made to suit the axles.

Do you need the gcode to turn them? The Mach3 wizards are limited in that each wizard is designed to do one feature only. You can combine the code from each wizard by cutting and pasting into a suitable text program but complex forms such as the wheel need a bit more skill than cutting and pasting sections of the code produced by the wizards. You don't say what equipment will be used, does it have an automatic tool changer for example? Is the lathe picture the one you are proposing to use? Can you fit a 4 jaw chuck or a three jaw chuck with soft jaws? Does it have a collet option? Does it have a home function?