I think that, the early 2000s would be a fine time to have an animated series when the cast is established, where spinoff games basically demonstrated what are the significant characters going forward. I am thinking of how Daisy returned to prominence, and how Waluigi was introduced. The characters might not have much to work with but that allows them to do what could be fit for them. Though Super Mario Bros. Super Show operated during a time where characters didn't have a well-established identity, it was enjoyable all the same.
More than anything though, I prefer a comic or graphic novel featuring the series. It would ideally be anthological, as in featuring different unrelated stories because the Mario series doesn't follow a canon, and thus a new story shouldn't rely on knowing past events to be familiar with them. I think this is the best way to go about it, and potentially, the less-major characters could even get the spotlight! Super Mario kun might have been seen as the comic for the characters, but it's clearly going for a different style and audience, while I think something that would be enjoyable for a wider range of audiences would be something I would like.
You know what would be a fun idea? A radio play featuring the characters! It's something Japanese voice actors do more regularly, and while the Mario series have cartoony voices and probably not fit for drama, I would be open to something like that. I am already one of those weird people who like to hear Mario talk, liking that 3DS video and even that Mario Press Conference, so a play where he makes comments on a variety of things and settings would be quite something.
Thank you for reading.