With very few exceptions, the first time I print a “final” print it is a .psd printed from Photoshop (I make further prints, when necessary, from Lightroom).
I use layer comps a lot to document my work in Ps, especially the states I’ve proofed along the way. When I make my first “final print” I document the paper and size (i.e. paper size and image size), as well as the date printed, in a layer comp. I used to use the note tool for this information, but once I became comfortable using custom workspaces I made one showing layers, layer comps, and other panels in a comfortable format.
In Lightroom, I use keywords and smart collections to keep track of all the “final” psds. Actually, I use the keywords “Done?” (yes, with the question mark, since “Done” feels funny for me to use when I can go back and rework something) and “boxed” as well as keywords for the paper size (and, for each paper size, the image size) and for the actual box in which the print is stored.
With all the smart collections that can be made from this keywording as well as my subject keywording it is has become easy (if now somewhat routine and tedious) to keep track of my favorite printed images.
As far as losing track of important files is concerned, as you say, it’s a workflow question. What I’ve described will work for me only if I don’t lose track of the favored .psd.
When I want to keep a paper record of something new that has worked in developing a file in Ps, I make a screen shot of the layers in question (and sometimes annotate it after printing) and keep in the appropriate folder in a filing cabinet, sometimes taped to the back of a print of the image (on letter size paper, of course).