Best Approach for Achieving PS1 Styled Rendering?

Hello, I’ve been using Unity for about 3+ years. Nothing really serious, but recently I suggested Unity for our studios first game. The goal of the game involves creating a rendering style similar to old consoles like the Play Station 1. 2 screen effects that I would like to emulate would an interlaced television screen and the Playstation’s lack of Z-Buffering creating the look of “squashed 3D” or twitchy graphics. The interlacing effect I believe can be done with a render-to-texture effect however I’m not sure. The lack of Z-buffering effect however is what puzzles me the most as I have no idea where to start looking to achieve this effect.

For reference this is the look I’m talking about.

For me the things that stand out most in that video are the lack of perspective correct texturing and low precision in the vertex transforms.
It is possible to switch off perspective texturing in DirectX/OpenGL though I’m not sure if you can do it in ShaderLab. To emulate this you would probably need to do something in your vertex/pixel shader to undo the perspective transform.
To get the low precision vertex transform effect you could try quantising positions at some point in the transform pipeline (clip space would probably be best), you can do this using the ‘floor’ function and some scaling in a shader.

There is some info on affine texture mapping (no perspective correction) on wikipedia:

For a quick easy way, just set all texture filtering to point. It won’t twitch much but it’ll look maybe crap enough for your purposes.