I mostly am just a casual player during the main game. Meaning I don't catch 3 of every Pokémon with a living dex in mind. However since Y is my only game to really compare.
When I started Yellow, Crystal and Sapphire, I mainly got to the end using my starter only but was without a good enough team to battle the final 4/champion. So I set the games aside, then many years later I went back to these games and put a team together using what I had in my pc or trading Pokémon to the game, ie in Yellow I traded a Kadabra and Seel from Crystal and used those as my starters. In Crystal I found a cloned Croconaw and a Jynx in my pc and leveled them up in Victory Road in order to help out my only good Pokémon Typhlosion.
I think when I was a kid I wasn't really playing to complete the game, but rather just to play.
Now for a team I like using underdog Pokémon, in Y I used Klefki and Emolga, in Omega Ruby, I'm using Linoone and Mightyena.
Of course I didn't think about shiny hunting before Y, mainly because I don't think I knew they existed.
Now in Y my only goals are shiny hunting and completing a living dex.