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to be really accurate Red, Blue, Yellow, and Green were built for the gameboy pocket.
Gold and Silver were designed for the Gameboy Color. (although they were still usable by the Gameboy/gameboy pocket.

As for the anime, I'm not a fan of any of it personally.
There is a Manga, the Show isn't based off of the games despite what people might think. The games, and the manga actually go together. (In the show Red/Ash, never caught a Eevee that was genetically altered and then evolved into a Espeon, but in Silver, Red appears with a Espeon in Mt. Silver as the final opponent.
The most commonly known is Pokemon special. Where Red and Green are the Rivals from Pallet Town. Blue and Yellow don't show up right away. Silver is the son of Giovanni. Berlitz has no game of her own (to our knowledge), Koga is a member of Team Rocket, and hates Green for chopping his Arbok in half with a Scyther.

The original games are classics, G/S/C did update the R/B/G/Y games without adding anything that people have complained about. (besides a few pokemon) Generation 3 and 4 have made some larger changes, but are overall not that bad.
If your stuck on using the G1 and can't even look to the G1.5 (which is what I call the G2 pokemon games considering those two generations are the only ones that conicide with anything of previous games aside from some mentions, and pokemon species.) then you are missing a few things. Nothing that is absolutely necessary to enjoying the gameplay, but they have been adding more and more gameplay distractions every generation.
Me, I think that G/S/C is probably the best of the generations, but hey, that's just me, and I have some logical reasoning for why I think that. I'd get into details about that, but this post is already getting rather long.


Also, I'm angry that you didn't include Green Version. as one of the original pokemon games. (Red, Blue, and Green versio nare the originals, with Yellow being made to connect with the original TV show.

the magna is great u should really read it