The nearly ideal box was already in my recycling bin. It had:
- Correct width (but 6cm too long)
- Thin cardboard
- Viewing window
Thin cardboard is easier to cut precisely, and it allows the connectors to protrude a little. (The shipping box, with thick cardboard that is doubled-up on the ends, would have ports very recessed and harder to access.) Also, thin cardboard might also help with cooling, and make it easier to use the On/Off button.
A box that's long is fine, but too wide would be a problem. You can easily cut a long box down to size, as I did. The wrong width would allow the Pine64 to move around, perhaps, and make it harder to access the microSD card.
A viewing window is a nice luxury. It allows easy visibility of the LED. In a dark room, though, that red LED is bright enough to show, even inside a closed, cardboard box, assuming you've cut holes for ports. At least one of the holes you cut is going to be a little big, or slightly in the wrong place. At least, that was my experience.
Other considerations you may have:
- Temperature / cooling
- Protection from:
- Static
- Pressure
- Spills & humidity
- Dust
- Space within the case for LCD, access to GPIO, Euler, battery, etc.
- Access from GPIO to breadboard
(click to see full size)

This case should meet my needs until I start using the GPIO. It protects from static, bumps, drops, spills and (somewhat) dust, while giving access & protection to the microSD, and access to all the cables.
I've detected no overheating, while using all the OS's mentioned in my signature, with the room temp as high as ~28C (82.4F). I've been able to play YouTube videos fine. Arcade-type video performance has not been good in Debian Linux. I'll test that again, the next time I use another OS.

In hindsight, maybe cutting the hole for the On/Off button wasn't needed. Can't you just press through the cardboard? The hole helps my finger find the right spot to press, I guess.
By coincidence, the Pine64's headphone/microphone jack ended up right above the phrase "HD Audio" and in the center of the headphone logo.
The box isn't perfect, but it only cost me time, it saved a box from the trash, and most importantly, the Pine64 is safer.
Hope this helps someone!