How do I create a "Pokedex"?

I am using the term “Pokedex” as a shorthand because I think it conveys the idea best; essencially I want to create a Monster Manual/Library, where after having the monster spawn at random from an Object Group,

(Something like this)
that monster will be added to a list of encountered monsters (and presumably have stuff unlocked like the Pokedex does)
How would you go about making that?