Welcome to ZenziWerken
In many cases birch or beech plywood is the material of choice. Multi-part-assemblies are glued with classic wood glue and surface and edges are sanded. Sometimes the surfaces are treated with wood stain and/or hard wax oil. Other tools are rarely needed.
Like 3D-printers a desktop-cnc-machine is an adequate tool for making toys and decoration. The size of the machine bed forbids the production of furniture. But other than a FDM-printer the variety of materials is much greater. Besides various woods, you can work with synthetic material (like PVC-Foam) and metal (aluminum, brass) and even compound material (aludibond).
The construction files were created using Solid Edge 2D Drafting or Adobe Illustrator and can be downloaded directly or at Thingiverse. As the creation of the files and realization of the project takes really much time and quite some money, I'd be grateful for some donations. At the moment the downloads are for free. The amounts besides the buttons are suggestions.
The commercial usage and the circulation of the design-files is specifically prohibited. Deep linking not welcome. If you think about commercial use for a fair share I am open for discussion.