Jethro, for DC motor you will need more complicated servo electronics, to stabilise rotating speed.
Arduino controlled stepper is a good and very versatile aproach - but a bit more complicated, and I have a feeling you are not comfortable with hands-on to those things... that is why I suggested AC motor with (or without) transformer.
If it is "wrong" speed (50-60Hz issue) this is easily mitigated with suitable dimensioning of the mechancal design (the whole thing on UK website you mentioned earlier is designed such that you have to turn the knob once per minute, listerning to 5-sec beeps (and moving handle by 30°) or watching the seconds hand of your wristwatch)
Good source of gears are old trashed printers, scanners etc.
Also you can try
Small parts,they have a lots of other stuff.
On your latest pictures - I think they are out of focus. You may want to use Bahtinov mask to achieve better focus.