I generally try to only use Pokémon introduced in the game I'm playing - its why I prefer BW to their sequels, which is a minority opinion I know, as the sequels give you lots of older Pokémon in the early stages. I'll make an exemption sometimes, for example I used the event Pikachu in my current Violet save, and when I finally play XY I'll have to use some older 'mon to get Megas (but probably not the Kanto starters, given I have all of them in Gigantamax form in Sword). As a kid I always used the box legendary, then went through a phase of not bothering. Now, particularly as there are story reasons in the likes of BW and SwSh, I will use them the first time out. I'll usually avoid type overlaps, but I don't mind if I lack coverage. For example my most recent Platinum and Shining Pearl teams didn't really have much to get past Lucian, just one or two super-effective moves:
Platinum
- Empoleon
- Staraptor
- Luxray (Crunch)
- Roserade
- Lucario
- Rhyperior
Shining Pearl
- Torterra
- Infernape (U-turn)
- Empoleon
- Go Shiny Lopunny
- Garchomp (Crunch)
- Go Shiny Magnezone
Before I vastly expanded my game and console collection, I also made an exemption to my rules for evolution-only Gen I-III Pokémon, as I had no way of trading between my LeafGreen and Emerald files. So my last HeartGold team featured Gengar and Machamp. Then also a Vileplume as I found a shiny, which back then is extremely rare and in fact was only my 2nd ever!
I found myself more and more going beyond the 6 'mon limit in order to enjoy the weaker gimmicky 'mons. For example last time I played Emerald I wanted Salamence and Milotic on my team, both of which due to location and needing the Blend Master respectively weren't available until late on / post-game. So I also had Wynaut and Castform in my team for the first run through - Wynaut lost her place once I could breed a nice Bagon, and Castform made it to the Hall of Fame (messing with the weather really hurts the Ice and Water teams at the end) before giving way to Milotic. Notch-Eared Pichu usually gets some time on the team in HGSS too (despite being lv. 30 its not OP against Whitney due to being a Pichu). Which is good, because I can get quite stuck in my ways but feel that the newer games definitely intend you to have one long save using lots of different 'mons rather than constant replays. So in my Violet save I've already dropped Oinkologne in favour of my shiny Dreepy (again, breaking another of my rules).
On previous occasions I've also just copied the manga characters' teams, which can make for a variable difficulty level - Red and Blue have strong teams that power through Kanto, whilst Silver (Sneasel / Kingdra / Murkrow / Feraligatr / Red Gyarados / Ursaring) could likewise obliterate Johto but Gold's team is far weaker (Aipom / Typhlosion / Politoed / Sudowoodo / Togepi / Mantine / Pichu). With the latter I didn't even bother with Mantine, so need a lot of revives to keep Sudowoodo in the game against Lance!