Fun question! I think the tl:dr answer would be I decide based on the version exclusives because a lot of my favourites in a gen keep ending up as version exclusives and I want to use them on my first playthrough, but how I picked each game was more in depth and didn't have a same answer? Here are my very tl:dr thoughts on why I picked each game per gen.
R/B/Y- technically my brother got this one but yellow because it came with the pokemon edition GBC
G/S/C- crystal because it was the third game??? Could be female trainer? I was a kid and at the mercy of my parents so I couldn't just go out and buy one whenever I wanted? Can't remember. Though I vaguely remember kid me wanting the third version before Crystal was announced because I expected you would be able to get an exclusive starter and then all three starters like in yellow, clearly my kid logic was not right.
R/S/E- emerald. I initially was not fond of Hoenn because it felt like a downgrade, they took out day and night visuals/weekly events, no Pokemon animations when you enter battle (I was a petty kid lol) and on top of that we couldn't transfer our old Pokemon over?! The reason I decided to pick up Emerald was no joke because they animated the Pokemon again.
FR/LG- originally skipped because I was done with new Pokemon games (came out before Emerald and all). If I recall I actually bought this after gen 4, needless to say I didn't get to choose because they only had LG in stock (and thinking back, I was pretty lucky they had a GBA Pokemon game at all). If I picked myself I would have gone for FR though since growlithe is one of my gen1 favourites.
D/P/P- first time I picked up a game before the third one launched, amazing! I picked Diamond because I liked the version exclusives better.
HG/SS- heart gold, I can finally catch my own growlithe in a game!
Also while legendaries almost never sway my opinion (I don't use legends on my team) Ho-Oh is the cooler Johto bird.
B/W/2- white, preferred the exclusives (braviary <3), and also white forest interested me more for end game since I prefer collecting/pokedex completion over (competitive) battling. Black 2, so I can have the other exclusives (and no Reshiram whoops)
X/Y- X. exclusives again, specifically swirlix.
OR/AS- (I completely forgot these games existed for a hot minute and almost skipped them in this list). Went with OR for exclusives probably? I was going to originally skip this but ended up buying it on sale because I figured it would be more convenient to replay Hoenn on a 3DS vs GBA. Which...was still a waste because I don't even think I got to the third gym. (I swear I don't hate Hoenn but I guess I have little attachment to it considering my childhood impressions)
Sun/Moon/Ultra- sun, I wanna say for the exclusives but I for the life of me can't even remember what they were (I'm almost positive I bought it myself and it wasn't gifted though)??? Ultra Moon for the opposite exclusives. (never even finished this one whoops, I was pretty disappointed it was just a third game but they cash grab released two versions? I was expecting a sequel like BW2. Regret buy u_u)
Let's Go Pika/Vee- skip. I hate go and don't want it in my Pokemon games, plus I don't really need to play yet another Kanto remake.
Sw/Sh- I was going to skip this gen because I was adamantly against the no national dex. But my brother got me Sword as a Christmas gift (I did enjoy it for what it was at least, plenty of new Pokemon I do love a lot, but still hate I can't have an Oshawott in this game). For what it's worth I didn't bother getting the DLC nor plan to.
BD/SP- skip. I was planning on getting one and just never did whoops. Don't really feel like I'm missing out on much though, maybe if I find a used copy for really cheap.
S/V- I was still debating on which version, first time that I didn't feel any strong opinions for either version exclusive lineup, I liked Koraidon more than Miraidon, and the past theme over future, but liked the violet uniform way more (why are we stuck with four outfits and they aren't even neutral colours, nothing goes with these ugly bright orange striped shorts/pants u_u). All debating cut short because again, I was gifted Scarlet for Christmas haha.