Two hardware components suggested to me for building a low cost educational computer are the Intel PXA270 processor and a single board computer such as the Gumstix.
The PXA270 has an Enhanced LCD and USB Controller built in.
Gumstix are one of the many single board computers available. These are designed for hobbyists and for incorporation in small scale production of devices. They typically have a range of expansion board allowing a complete computer to be built (or built into a piece of equipment).
Another interesting product I found was the Motorola TXTR D7. This is a wireless SMS terminal for a mobile phone. The unit is 54 x 18 mm with 4 lines, 20 character screen, rubber Qwerty Keyboard. It is intended to communicate with a mobile phone via Bluetooth for sending and receiving SMS messages.
The Motorola TXTR D7 does not seem to have been successful as a product, but a terminal with a bigger screen and keyboard may be more viable. Those who want a very small QWERTY keyboard for SMS will probably just buy a smartphone with a keyboard built in, rather than an extra external to carry around. However, a more capable device with a larger 5.6 inch (A6) size VGA screen and keyboard might be of use. This could be used for web browsing as well as SMS. It need not be a fully functional computer, as it can make use of the processor in the mobile phone it is communicating with.
This device might be made inter-operable with the Microsoft Ford Sync car computer. It could then be used for playing music and video from a mobile device as well as operating a mobile phone remotely. This could be built into a car dashboard, used in the home or made as a portable device.
I have put this up as a suggested new expansion board for the Gumstix.