my advice is based on my experience following JB’s advice.
substrate just comes down to what you want. i’ve done mostly 1/8" BB, but did do one on chipboard. i know JB has done 1/4" BB, too. for image, the finish comes down to what you prefer. i’m not a glossy fan, so i use satin photo paper. but glossy will work. same for the varnish, whatever paper you use, the varnish finish should probably be the same.
windsor & newton is what i’ve used to varnish. i used brush varnish on the first couple of times, too. spray is easier and less potential of streaks.
depending on how much you care about a minor amount of burn at the edges and how much you want to clean the pieces, you can get away w/o masking if you do a good job of sealing with varnish. i’ve found it’s less work to mask if you use the mask twice and cut horizontal and vertical in separate jobs. mask, cut horizontal, pull off. remask (without moving the puzzle in the bed) and cut vertical and outside, peel off. then remove puzzle.
take the puzzle off the crumb tray and put in a bin with salt. and, as eddie murphy once said, “shake the **** out of it.” remove puzzle from salt (this can be done with something similar to a colander, but if you’re not doing multiple puzzles, you can just pick them out instead of dedicating something like that).
personally i go one more step and create a box with the lid proportions of the puzzle (i.e., puzzle is 16x20, you can make an 8x10 box or a 4x5 box, just have to figure out how tall it needs to be) so the photo of the puzzle will fit perfect. i use boxes.py, but plenty of options out there. glue photo to lid.