Just a quickie on my setup in Unity for a 3D game.
I have two cameras. The main camera is othographic and is looking at a texture with the correct aspect ratio with a black clear colour. This means all renders the game correctly by just looking at the quad in front of it and fills any extra space up with black.
The second camera points at the scene. It has a full screen effect that pixelates the screen to the correct resolution and limits the colours to four I like that are sort of like the gameboy. This is a 3d camera and renders to the texture the first camera looks at.
This setup allows me to render a 3d scene that looks like it was created with a gameboy. By carefully choosing materials and rendering an outline around stuff and on creases it should look alright but be quicker to set up and get working than writing a proper shader to do dithering.