Grass, Fire and Water.
Every generation, a new trio of Starter-Pokémon are introduced, and after the cover-legendaries, they're the closest to being the mascots of their generation.
They're the first Pokémon you obtain for your adventure in every main-series game, and because of that, Gamefreak takes more time for their designs than for most other Pokémon in an attempt to make them as balanced between friendly/cool and as appealing as possible.
It's one of the most fundamental traditions in Pokémon.
The reasoning behind their primary types is that they are meant to convey the mechanics of the type chart to new players, since Water being strong against Fire etc. are some of the most intuitive examples of type-match-ups.
Starter-fatigue?
When a generation meant ~130 or more new Pokémon designs, a new set of such traditional starters at the beginning made perfect sense. However, with the 6th generation (X&Y) being the smallest in size (~70), the newer starters make up more than 10% of the generation. And if current speculations turn out to be right (that Sun&Moon will start another short generation that acts like a second half to Generation 6), the ratio of starters is going upwards. And the fact we've seen this trio of elements/colours/themes 6 times in a row, doesn't help in keeping the concept exciting.
Of course there is still the option of simply NOT introducing a new set of starters and using the ones for Kalos a second time, but anytime a new generation is even just hinted at, the hype surrounding starters is too big and important to be confronted with that level of disappointment.
So I thought...
What if "Sequel-generations" used an alternate set of starter types?
There would still be the standard new Grass/Fire/Water starter-trio we all know and love for the "main generations", but a different set of types (perhaps even different each time?) for when there is a shorter "sequel generation" (like possibly Sun&Moon) after a shorter completely new generation (like XY).
It would be exciting and refreshing to see the "luxury" (of a guaranteed inclusion of a well-designed 3-stage Pokémon) extended to some other types for once.
The weakness/resistance-cycle
Not many groups of three types have that signature triangle of weaknesses with each other one way and resistances the other way that Grass/Fire/Water do, but that's not a surprise, considering that they were designed with that in mind.
The only 2 other suitable trios (Rock/Flying/Fighting, Fairy/Fighting/Steel) therefore feel rather arbitrary and unintentional.
That's why it would make sense to leave that aspect out for an alternate set of starters altogether (Another option however could be to make sure the types have neutral match-ups with each other).
It loses the "type-chart introduction"-part, but since that's only relevant very early in the game anyway, an obvious and convenient solution to that would be to demonstrate type-advantages with the elemental monkeys from Generation V. Anyhow...
Let's look at some examples.
(I'll use silhouettes of existing Pokémon for demonstration purposes. Think of them as silhouettes of new Pokémon with similar basis, which would act as the first of a 3-stage starter-like evolutionary lines of their respective type.)
The first possibility that comes to mind , is taking 3 just as colourful and elemental types as the traditional ones.
- Electric is a perfect replacement for Fire, being the other bright energetic type in the selection (well demonstrated as opposites with Reshiram and Zekrom). With Pikachus fame and role as a pseudo-starter, the types suitability is even more evident.
- Ice is another high priority choice, due to the type having just as much conceptual potential, while getting barely any attention in terms of basic Pokémon-designs. It would benefit extremely from being a starter-type, whereas Water is already the most common Pokémon type altogether.
- With those two acting as Yellow and Cyan, the appropriate choice for the third type would be Magenta, hence Psychic, which is not out of place, being a more direct "supernatural abilities"-type. And while it has had a handful of relevant 3-stage lines, none of them have taken on the "Psychic" palette that is supposed to be it's cliché-colour.
(and they also happen to not have any relations with each other in the type chart, which makes them even more of a favourite example).
Another set of types that could work as an "advanced starters"-type-trio, would be 3 types that are based around a strategy/approach to battling rather than clear elements.
And while the old fan-idea (that sort of got realized, as secondary types for the Kalos starters) of Fighting/Psychic/Dark as a trio is a good match, I'd personally switch out Psychic for something as gritty/grounded as the other two types: Poison (a type that's also rarely featured with an important 3-stage line, or even as the primary type in a Pokémon in general).
For the third example, the underlying theme is "creatures".
As a big contrast to the traditional starters (which tend to be based on more familiar and pet-like animals), the alternate starters could be of the types that relate to a Pokémons own biology.
by one of them being perhaps a beetle or an arachnid (Bug type), a prehistoric animal or a mineral-based lifeform (Rock type) / a metal and alloy based, perhaps artificially created lifeform (Steel), an extraordinary supernatural creature (Ghost or Fairy), or even a mythical Dragon type.
