As for scenarios for each character and how they come into the fray, how's this:
We at least know 2 things. Egon is in Geneva doing research and GB ceased to operate sometime between the game and now for unknown reasons.
Perhaps since then Ray has taken to doing college lectures around the country on the paranormal, based on all the new things discovered during his tenure as a GB and of course research in his personal life. Early in the film, we first see him as he is giving a lecture at a college. It's your usual crowd. Some are interested, some think it's a joke, some are just here cause they were told they'd get extra credit for going and taking notes, and some are hanging on every word. One such student could be Allison Scagliotti's character. She is eating every word Ray puts on the plate and then licking the plate, taking all kinds of notes. Her friend sitting next to her is watching her, wondering if she'll explode. He is an average looking college kid with blonde hair, who is decently engaged by the material, but is more entertained by his friend's drooling. He asks if she's gonna be ok or if he should find a defibrilator just in case, but she quickly shushes him. But there's something about the guy...he's familiar, or at least he should be.
Later on, the lecture ends and Ray asks if anyone has any questions. The girl nearly jumps out of her seat and is about to ask a question, when her friend cuts her off and proceeds to ask Dr. Stantz what ever happened to the child that they helped during the Vigo conflict. Ray squints into the lecture hall seating to see who asked. He grins when he recognizes the student: Oscar Barrett.
Later, as the students filter out of the hall, Ray greets Oscar with a warm hug. Oscar introduces his friend to Ray. She gushes. Not only is she a fan of the GBs, but also a student of the paranormal, as she impresses Ray with her knowledge, and also with the intelligent questions she asks.
So that's how we'd meet those 2 characters.
Maybe another could be a someone that Ray hired at some point to take over at Ray's Occult book shop when he could no longer successfully balance his duties as both GB and shop keeper. Also having an interest in the paranormal, Ray gives him sort of the "Ultimate Promotion" when the time comes to assemble the new team.
PS
Extreme Ghostbusters was an epic win. I loved the animation in both it and the MiB cartoon.