I am not really in a position to offer advice, but I would encourage you to think again about building your own cabinet.
I struggle putting up a shelf in my house, but I've just finished my first cabinet. I didn't break the bank buying tools, and to be honest it wasn't that much more difficult than putting together flat pack furniture once you figure out how you are going to build it.
I had so much fun building mine and it is so much fun to play.
In regard to what you put in the cabinet, I've used a Raspberry Pi 3 b+ in mine with RetroPie (
https://retropie.org.uk/) installed. The pi was cheap, easy to set up and ideal for the job.