Ed, even a phone could be a complete computer system, but still very expensive (for a nice screen and imbedded keyboard). If you want to go the inexpensive route, you have to compromise with the kind of devices that the computer will have. There are tons of single board computers out there, all with their own characteristics. Using the onion, you can add the OLED as display, and a few buttons as input, and off you go. It's very limited and requires imagination, but it certainly is possible.
Kit, I love your Pi-Top suggestion. This one could be an excellent gift suggestion as well.