Search for Spock might be the first movie (in general I mean, not just Trek) that I can clearly remember watching. It was 1990 and I would have been five years old, was at West Coast Video with my mom and she must have randomly picked it off the shelf to rent.
Watched it, loved it, was hooked from there on out. Rented the other movies, even rented Encounter at Farpoint and the uncut The Cage that goes black-and-white during certain scenes. TNG became appointment television every week. Saw TUC in the theater and was blown away. Didn’t even get into Star Wars until around '92 or so, but I knew of them as Bart would say.
What I remember finding out very early on was that ILM worked not only on Star Wars but also several of the Trek films. It felt very cool to realize these two franchises shared that connection.
Oh, and thank you for bringing up Oberth class, SwissArmyTin. I was going crazy back in September trying to remember the name of it without looking it up first.