Hey!
Before i go any further, will you be provided with a screen similar to the one you linked to? Because most of these come already packed with a microcontroller to easily program them.
Else:
If you're going to build the LED grid yourself or will have it pre-built but without any microcontrollers or anything with it, i recommend you use an arduino as it (much) easier to use than the raspberry pi and it has more pins than it as well.
*Note*: An Arduino is a *MicroContoller* while a Pi is a *MicroProcessor*
What you're asking for is quite simple in concept but it requires a few other processes to be well-executed, so i'll have a rundown of things to consider:
-How big is your grid? The arduino has 14 digital pins and 5 analog pins, giving you a total of 19 pins. To increase the number you'll need an IC (integrated circuit) called a Shift Register. Normally a shift register has 7 output pins(you might find more or less), meaning each pin on the arduino will now be equivalent to 7 pins. and shift register can be connected to other shift registers as well!! But with too much connections, delays might occur..... so lets stay reasonable.
3 pins will go to your buttons. so you have 16*7 = 112 pins to use.THAT'S ALOT!!
- multiplexing: ofcourse when you have a grid you can connect each pin to a LED individually , but that's simply inefficient. So we connect each pin to a row and another to a column, and the LEDs are connected in a matrix. This video does a sufficient job in explaining it.
https://www.youtube.com/watch?v=MmCGDJ90Qt4
Here's a tutorial for a small grid:
http://diyhacking.com/arduino-led-matrix/
After that it's just trial until you find what you want to display, and then make each button play a function that displays the display you want.
If you need more help please ask!
Don't PM me, but instead post on this thread so everyone else benefits :p
Good Luck!!