The paper I use is called "presentation paper". It's glossy, similar to the paper used in magazines, but a bit thicker. In fact you can use magazine paper instead and get it for free.
I bought a pack of the paper back when I was making my own circuit boards regularly, so I'm not sure if it's still available today. I tried several types of paper at the time and that one gave the best results.
I use muriatic acid and hydrogen peroxide, but there is a "proper" etchant (Ferric Chloride) you can get to use instead.
My usual procedure was to etch and clean the board, then tin the copper traces completely and then drill the holes for the parts.
The video thumbnail image is an example of a more complex board I made using this process.
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