The hand will display the hour of the time by raising or lowering fingers. (I.E. just your index finger raised will be 1:00).
If it's supposed to be a binary clock, don't demonstrate it between 1:59 and 3:00 (a.m. or p.m.), unless to someone you really hate (preferably someone smaller than yourself)
Some nationalities may not like it from 2:59 to 4:00 and yet some will find 8:59 to 10:00 a bit offensive.
Call it a World Clock and you can P.off people day and night
I also wanted to include a simple screen that read off the minutes.
Simple is good... What do you call "a simple screen"?
Two 7-segment LED displays would be better/simpler than a screen.
I was wondering how to control all of this? Is the control and program seperate entities?
The program controls it all.
As you can tell by the name, I am completly lost in this field and would like a slight push in the right direction.
Here's a push: Start with a single finger and make that work as you want before you proceed.
You need some sort of a microcontroller board to stuff the program into - do you have one already?