in terms of size I'm currently looking at around 64X64.
Inches? Meters?
So long as you're not 64mm size, this is likely to be a custom build. Grab a piece of plastic and some backing material that's waterproof. Stick down LED strips to the back. Test it works. Then seal around the edges. Strangely, it's significantly cheaper to buy the LEDs in strips instead of individually, even if you're buying in bulk. You may even find you can get waterproof strips, which means you only need to seal the connections to the ends.
The MEGA does not have significant extra analog capability except for a lot more pins. That's useful if you're trying to drive LEDs individually. Not useful to you since the number of LEDs will exceed the number of MEGA pins, so you have to use smart LEDs or some other port-expander device anyway.
Buttons sound like a good idea. But get it started connected to your PC and sending commands over Serial.