The way prices are, the mechanical things you build robots from are a lot more expensive than the electronics. Fabricated steel or aluminum is just expensive. A lightweight gripper, powered by a little servomotor, is $20. https://www.sinoning.com/collections/manipulator
Plastic gears work well for light duty. But I find that NEMA size 17 steppers have a lot of torque, much more than plastic gears can handle.
Steel gears start at $6, and you always need a pair, and the shaft mounting must mesh the teeth with a precision about +-.2mm when you are using 32 pitch. At that rate, one shaft of a pair of shafts must have an adjustable mount, when you are mounting with wood. So the gear scene doesn't work well for me.
I looked at what is plentiful at Marlin P. Jones and Associates (MPJA.com), 2mm-pitch cog belt. Some of these parts are available in quantities of 10 through Amazon at good price. Idlers and toothed pulleys are shown in the photo, and ball bearings. The shaft-positioning tolerance doesn't matter when you can throw in a tensioning arm.
Shaft size is commonly 5mm. You see some 3mm, like on smaller stepper motors.
If cog belt is good enough, then you are faced with what to mount such parts on. I am pretty much limited to wood, I have no room for metal machining. Wood can do a fair job but it doesn't look all that great.