https://www.bostongear.com/pdf/gear_theory.pdf
This should help with some of the clearance (backlash?) questions you have, as it would have been what I would use for reference. If you have a copy of the Machinery Handbook it would also help and provide guidance. I had said Pitch Diameter, but really the Diametral Pitch you choose for the gears determines what diameter you have, as well as the amount of backlash you should expect, though the criticality of the backlash is only if you are going to move the mechanism back and forth often.
Also keep in mind manufacturing tolerances tied to the machine you are making them with. The teeth may grow or shrink due to this, either increasing or decreasing the clearance you experience.
I would also recommend not making gears out of aluminum unless you plan on anodizing them. Aluminum on aluminum tends to gall.