You could use shift registers to clock data in/out of the computer.
It depends on you using the data synchronously, which means you need to provide a clock signal in parallel to the serial data stream.
8 bit shift registers are easy to use, and if you require more than 8 inputs, then cascade them. I.E. two of them in series will give you a total of 16 inputs.
You could probably use the joystick port for this, you can send data in/out of there in the same way the AirLink IR tranceiver works.
As for the display, personally I find serial LCDs a lot simpler to use, as the driver and everything is all built in.
You just need to send the correct setup and control information and you're in buisness.
Haven't played with them under AmigaOS, but have done using microcontrollers such as the Motorola HC11. Using a PIC to do some of the work for you would make it even easier. You could address it using asyncronous data via the serial port.
A few guys have used these in Amiga based car audio players. See how they do it. I saw some good circuit details on one of these sites.
