We should probably stop categorizing things as geek media. It's an old idea that really just means outside the old american monoculture. With the crumbling of that monoculture, media really isn't geek or non geek anymore, it's just media. Now saying that, I'm old and know exactly what "geek media" means and my list of formative media absolutely fits. I just feel the need to put out that disclaimer.
The Transformers: My first love. I was very young when it came out, and my first memory is getting an Optimus Prime for Christmas. While I liked the series a lot, it was the toys that really stuck with me. They hit the perfect middle ground of fun thing and engineering demonstration for me. Transforming toys are an art form deeply intertwined with technical engineering knowledge. Growing up Transformers media became less important, but the toys only grew. Now I'd say collecting transforming toys is my primary hobby.
The Lord of the Rings: My father read books to me as a child, and one of my favorites was the Hobbit. Being a reclusive smarty pants this led me to reading the Lord of the Rings in the 6th grade. That book really jump started my love of fantasy. While the I really do love the story, it's the world building that always stuck with me. The feeling that this alternate world actually exists beyond the story is something I really value in media.
Super Metroid: There are many games that I loved growing up, but Super Metroid hit me particularly hard. The primary thing that stuck with me was the atmosphere and environmental story telling. Super Metroid is a master class in immersion without breaking gameplay. Then on top of that it has incredible pacing, interesting puzzles, and incredible audio and visuals.
Batman the Animated Series: Is probably responsible for my love of the character to this day. It's a great series that takes time to delve into the psychologies of the characters as well as provide action.
Baldur's Gate: This was my first taste of the PC player driven, more simulationist side of gaming. The freedom given to the player in this was something I hadn't played before, and I was hooked.
Deus Ex: Then this game showed how far the potential of the player driven simulationist side of gaming can go. Few games to this day try to have a world this interactive and reactive. If you do something, the world and characters will probably notice and react to it. If you think you can do something you probably can.
Edit: somehow I forgot about TNG.
Star Trek the Next Generation: This was a family event for me. We eagerly awaited every episode and loved the series. It was a constantly engaging show, probably the first for me that tackled currently relevant topics. Most media I watched growing up had more general messages. Star Trek actively advocated for a progressive, better world.