Excellent, thank you both for the help!
That compatibility matrix is exactly what I was looking for. The signals that goes through the connector, how do they not conflict with each other? Is each shield on its own pin, with some form of serial protocol to transfer data? I've read through the TinyScreen library code (
https://github.com/TinyCircuits/TinyCircuits-TinyScreen_Lib ) and found that the screen can be on GPIO address 0x20 or 0x21. Are those addresses what makes sure that the shields doesn't conflict?
How many shields can the battery power? Is there a limit or is it simply a matter of how quickly the battery will drain?
As you can probably tell I'm still learning a lot about the hardware.

I am super close to getting a Tiny Game kit just to get cracking on the basics, but the big difference in clock speed and SRAM makes me wonder if I should get an Arduino Zero instead, and .. uhm .. yeah, I don't really know what display to get instead.

But if I have a 16 bit display buffer in SRAM then I could write an abstraction layer to blit it to any kind of display. As I would want to do for the joystick.