It's only take me 2.5 weeks to get around to responding to this myself.
Gen 1: Pokémon Yellow was my first Pokémon game. It was actually my Dad's copy that he let me restart, so I didn't get a choice in it! I don't actually remember making the decision to play this game, just remember the hours of fun I had with it.
Gen 2: Pokémon Silver. My Dad already had Pokémon Gold, so I asked for the opposite version. I then asked for Pokémon Crystal when it came out. When my Dad later got bored of Gold, he let me restart that too.
Gen 3: Pokémon Sapphire. I chose this one based on the box art mascot. I didn't really like Groudon at the time. I later got Pokémon Ruby as well - although this was because we were moving country so my parents let me pick out a new GBA game to play on the 13hr journey. My parents didn't let me get LeafGreen/FireRed or Emerald. I'd have gone LeafGreen based solely on the box art.
Gen 4: Pokémon Diamond. I liked Dialga better than Palkia. I then received Pokémon Platinum as a Christmas gift. I then went with SoulSilver over HeartGold - mostly for nostalgia as Silver was my first Gen 2 game.
Gen 5: Pokémon Black. I liked Reshiram more than Zekrom. I didn't really enjoy this generation so I didn't play B2/W2.
Gen 6: Pokémon X. Again, preferred Xerneas. Then Alpha Sapphire again for the nostalgia factor, as I played Sapphire first in Gen 3.
Gen 7: Pokémon Sun because I wanted the clock to reflect real-time day/night cycles. Then I went with Ultra Moon to get the opposite experience. Then I received Let's Go! Eevee as a Christmas gift, and at the same time my Mum gave my Dad Let's Go! Pikachu.
Gen 8: Pokémon Shield. I received both for Christmas, so I did some research on version exclusives and then offered my Dad the Sword version so we could play together. When BD/SP came out I was dating a streamer, so my at-the-time girlfriend bought them for us with her Twitch earnings. She wanted Shining Pearl so she gave me Brilliant Diamond.
Gen 9: Pokémon Scarlet. Picked mostly due to preferring the orange uniform over the purple. But I also liked the prehistoric Paradox Pokémon more than the Futuristic.
I miss third versions to Pokémon games.