So, personally, I've never had a CDJ, but I can tell you what I like seeing:
Personally I love seeing past characters—especially if it's a character the player can see themself using again. As for displaying characters, I like seeing some info (journal/link to their full profile if available, name, pb, fandom or game used in) but not a ton, especially if you attach their journal and it has info in it.
On that note, if you need a pretty to put them in let me know; I've been meaning to make something for displaying characters.