I think a good way to go about this would be to follow the same rationale that Red's team in both GSC and HGSS does: all starters, and guaranteed encounters that every player experiences. Looking at this a little more closely, we obviously have the three starters and Pikachu, representing all starters of the mainline titles of the generation. His other Pokemon across various games are Espeon (not obtainable in RBY, but represents the Eevee in Celadon), Snorlax (which you'll be encountering at least once to progress through the game), and Lapras (your reward for the mandatory Silph Co. plotline). These are all, for lack of a better word, safe choices that every player can identify with on some level. It also leads to some inherently boring teambuilding, especially with a constant and unchanging FWG core, but the fact of the matter is that starters are just too iconic to exclude. This may occasionally put us in a corner where we'll have to use past-gen Pokemon, but I don't think this is inherently a bad thing.
Just as a side-note, you could argue that Red having all three starters just represents the events in Yellow, especially with the unevolved Pikachu. Otherwise, though, the game tends to stick to RB's precedent, not Yellow's - Blue's team is identical to RB sans starter, for example - therefore, I think it makes the most sense to keep starters. With this criteria, I think the teams would be as follows:
GSC: Meganium, Typhlosion, Feraligatr, Togekiss, Steelix, Red Gyarados
Togepi hatches from an egg acquired from Mr. Pokemon, Steelix starts as an Onix from a trade in Violet City, and the Red Gyarados speaks for itself as a symbol of Shinies, a defining mechanic of Gen II. Togepi is the player's introduction to Eggs (and accordingly, breeding as a whole) and ends up starting your quest, so I think it's a natural inclusion. Steelix represents the brand new Steel type of Generation II. There's a bit of type overlap here with two Water types, but Red also does this in HGSS so I'm not too concerned about it. This unfortunately leaves the Dark type without representation, but I think this is a balanced team without that - though I should point out that Eevee from Bill can evolve into an Umbreon, covering that.
RSE: Sceptile, Blaziken, Swampert, Wobbuffet, Kecleon, Metagross
A Wynaut egg can be obtained in Lavaridge Town, several Kecleon can be found near the Fortree area (and at least two are encountered to progress through the story), and Beldum can be obtained from Steven in the post-game. While Wobbuffet is a Gen II Pokemon, it evolves from its Gen III younger relative, so I think it's a reasonable inclusion (especially with its defining ability, Shadow Tag - one of the greatest buffs in the series). Kecleon isn't particularly strong, but I think it's emblematic of Hoenn in many ways (a unique ability, an odd encounter method, and a complex color scheme); Castform could also replace it, but uh... no. Metagross represents the player character's friendship with Steven over the course of the game and rounds out the team with a powerful, iconic Pokemon.
DPP: Torterra, Infernape, Empoleon, Glaceon, Rotom, Chatot
Eevee can be acquired from Bebe in Platinum, Rotom can be found in the Old Chateau at night, and Chatot is an in-game trade in Eterna City. Glaceon and Leafeon are interchangeable here, but I don't see the need for two Grass types when we can represent Ice instead. Rotom is a highly memorable encounter with its unique setting and many forms, and Chatot has its fun microphone gimmick that harkens back to the DS era.
BW: Serperior, Emboar, Samurott, Volcarona, Emolga, Reshiram/Zekrom
Volcarona can represent either the Larvesta egg, or the Volcarona found in Relic Castle's deepest floor. Emolga is an in-game trade on Route 7, and while I've avoided legendary Pokemon up to this point, I think they become too central to the story starting in this game to ignore them. There's not a lot else to say here - these are fairly important and memorable Pokemon of the generation that all players will recall encountering on some level.
I think this team represents Generation V overall, but let's do B2W2 for funsies:
B2W2: Seperior, Emboar, Samurott, Zoroark, Gigalith, Reshiram/Zekrom
Whichever dragon the protagonist of BW didn't take, the B2W2 protagonist takes in return from N. Zoroark and Gigalith both represent B2W2's status as the first (and only) direct sequel games - Zoroark was formerly owned by N, and the Gigalith was the same Boldore that the player traded in BW for an Emolga.
XY: Chesnaught, Delphox, Greninja, Sylveon, Lucario, Xerneas/Yveltal
So to be straightforward about it - Sylveon is the first, and last, time I'll be breaking my pre-established rules. I simply think that Sylveon is a fantastic representative of the Fairy type, which is by far Gen VI's most significant new mechanic for the series. There are no guaranteed encounter Fairies besides Xerneas, who is only on the team 50% of the time. Lucario is the player's introduction to the Mega Evolution mechanic, another of Gen VI's primary traits. Xerneas and Yveltal are crucial to the story's resolution and are mandated captures, like Reshiram and Zekrom before them.
SM: Decidueye, Incineroar, Primarina, A-Golem, Zygarde, Solgaleo/Lunala
A-Golem can be acquired from a trade in Tapu Village, and represents Gen VII's introduction of regional variants very nicely. The Zygarde Cells were one of SM's and USUM's most notable sidequests, so despite being a legendary from a past generation, Zygarde makes for a natural inclusion onto this team. Solgaleo and Lunala, or should I say Nebby, are practically one of the main characters of SM's narrative, and so it only makes sense that they find their way onto this team.
SWSH: Rillaboom, Cinderace, Inteleon, Zacian/Zamazenta, Urshifu-SS/RS, Calyrex-IR/SR
So uh... Copperajah in the room (or lack thereof), lots of legendaries! Half a team's worth, in fact. I was conflicted on this, but really I just think this team makes the most sense, all things considered. The starters have unique Gigantamaxes with DLC, so I think they represent that mechanic on their own very well. Zacian/Zamazenta are like the version mascot legendaries before them, little need for explanation. Urshifu and Calyrex embody the two DLC areas added to Galar, and are very impactful on the narratives of these areas (Kubfu's trials to evolve into Urshifu, and Calyrex practically being the protagonist of the Crown Tundra). G!Slowbro or Slowking can respect Urshifu or Calyrex respectively if you have a distaste for so many Legendaries, but I think this team does the best job of encapsulating Gen VIII.