Maybe it's the fact I just woke up, but this kind of information doesn't rock my world. I assume you don't have a 3DS or any other Nintendo console apart from the GBC? I ask because I assume you simply never had the resources to play a Pokemon game, or you have and just found other stuff, because it's not all about Pokemon. For me it is, it's practically an everyday thing, trying to keep up with what goes on, breeding, catching along with soft resetting for the right pokemon, that takes up 99% of my play time. Right now on Sun for example, 555 hours and 8 minutes. It's similar with me and movies, I've never seen stuff like Casablanca and Citizen Kane, candidates for best movie ever made supposedly. Hell, the oldest movie I've seen so far is the original 1954 version of Godzilla. It can happen, never experiencing something that almost everyone has already, just shouldn't be negatively judged upon.
That being said, I'd go for Pokemon Yellow, I think it was the first Pokemon main series game made for the GBC. You have Pikachu as your sidekick, so some familiarity, surely you know the anime and who Pikachu is. Also, it's a Gen 1 game, simple to grasp the concept of only 151 pokemon, and then open the gateway eventually to 650 more. Downside is you probably won't have someone to trade with you so no Red/Blue exclusives, no trade evolutions, it wasn't until 2014 when I got multiple games and had multiple consoles that I experienced a trade evolution, and it was one of my favorite pokemon, Alakazam. It's a short game too, have to start easy. Crazy fact I never knew because I hadn't played the Gen 1 games long enough to notice or simply just finishing the story and not spending too much time post game. If your opponent is asleep, any recharging move has 100% accuracy, as in Hyper Beam! I think sleep also overrides the other major status conditions as well. That is crazy, maybe it happened to me in Pokemon Stadium but I never remembered, these are childhood games after all.
Anyways, after Yellow you can try out Gold/Silver/Crystal, Red and Blue if you'd like, hope you have the time. Given the limitations of the old games, for me they take notably longer to finish than the newer ones.