Whats a good way to get started building simple programmable robots with easily obtainable parts?
A well-stocked toy store or science store will have programmable robot kits that you can build. You can also get great parts from Lego and Erector motorized kits. Radio-controlled vehicles are another great source for parts. Stock Drive Products ( https://sdp-si.com/eStore ) is a supplier of great miniature power transmission products like gears, universal joints, bearings, clutches, etc.
