This is sort of getting away from the intent of your post a bit, but since you brought up first contacts, I would really like it if when you first meet a new race, you cannot know anything about them, and there is some system of sending a character to try to establish a connection and figure out each other's languages, with events that can increase or decrease tension between the two empires.
Just to avoid the whole 'Oh, sweet. You speak english.' phenomenon.
Yeah yeah yeah, Star Trek universal translator (*coughdeusexmachinacough*). But running into other races and not being able to know anything about them or communicate with them immediately does raise the mysteriousness and tension of the experience.
Yeah. I'm also always a bit annoyed by the whole "These are the YipYips - their race is 100% defined by the following traits and they will act totally predictable. We found that all out in the one conversation we had between discovering them and writing you this message"
Regarding first contact, I agree that this should be a major event for your culture, but also for small ones.
Everytime you discover a small species (especially the pre-spaceflight ones) there should be a random event how they react to it, with some options for the player. For example a very backward race might rever the player species as gods and you can either "affirm their beliefs", giving you a huge influence bonus but potential problems further down the road if they discover it, "educate them about the universe", leading to uplifting, "enslave them" etc.
The kind of events you may get, as well as the ways you can react to them, should depend on the traits of the race you discovered, as well as your own.
This could be mirrored for big Empire Contacts as well. If your first contact is an aggressive, xenophobic race, there might be a huge drive towards military spending in order to defend against the perceived threat, whereas if the first race you meet is friendly, there might be a drive for diplomacy and Federation (unless your own race is the xenophobic, aggressive one in which case there'll be a drive for enslavement

)
Well written Event chains where always one of the best things for me in Paradox games (and the main thing I would be looking for in Mods)