Getting started? What do I need?

Depending on what kind of display you want you may want to get some shift registers for multiple inputs/outputs ,
and/or actual display driver chips such as the max7219 for I think up to 8 regular 7segment led displays with dotpoint,
you'll need some transitors or preferebly mosfets(run cooler) to control any motor/servo/solenoids(andlook up flyback diode)
For lights you may want to look into higher power leds like common 1w leds, that bring constant current sources into play
that sounds like a very cool project
make sure you be very careful with your voltages,as I imagine this thing will get plugged in, line voltage is dangerous and anything that is plugged in has the potential to shock you, and always check that your power source is wired correctlyespecially if your machine has a metal ground, just today actually I plugged in a hammer drill to drive in a ground rod for a houses electrical service and whoever wired the outlet did so backwards, so imagine my surprise as I grab the ground rod and get electrocuted from one arm to the other, its not fun stuff and you don't want to be playing pinball and get shocked