First, I cut the wood for the frame, with a slit to hold the lid. The backside hs two holes (later actually four) for the power and USB connectors of the Arduino. The Arduino Uno is screwed to a thicker piece of wood.
I used this opportunity to try the new Laser engraver in our wood shop to add the Arduino logo to the lid. The engraving was not perfect, but it was a first try, and it's good enough for this purpose.
Two smaller pieces of wood are glued to the inside as separators to store cables. As an alternative power supply, I ordered a breadboard power supply (AliExpress, $1).
This has two inputs, one for a regular power plug, plus a Mini-USB connector. It has switches, and can be set to 5V or 3.3V. It sits on one of the breadboards.
That's it: my new Arduino playground!