Whatever you like. Pick your own scenario and build towards it.
90% of remakes disappoint me. As much as I like most of these characters, I want a new cast that is nevertheless rooted in the old.
Star Trek Online is a crappy video game with a great story. One I think I like is that because they use CGI, it's easier to have non-human characters so there are a lot more non human characters.
If I was in charge of a Star Trek series. I would set a rule that the number of full or half-human recurring characters can never exceed 50% of the cast. At least 20% of the recurring cast needs to be aliens that don't look like humans with very simple prosthetics (not too many Trill, Vulcans, Bajorans, etc) with the obvious exception that if an episode is going to take place on a Trill colony, then yes, most of the characters would be Trill.
Andorians and Tellarites are supposed to be founding members of the Federation along with humans and Vulcans but they are hardly ever seen. At least one member of the regular cast and at least one member needs to be one of each.
There need to be strong female characters, but they shouldn't be Mary Sues or straw feminists.
If
Guardians of the Galaxy 1 and 2 shows us anything, it's never been easier to make cool looking realistic aliens.
Every successful Star Trek show has an eye candy character. I say a Andorian. So she is not useless eye candy (like Deana Troi) and because Andorians have a warrior culture, I would make her the chief strategic officer if the show is centered on war or the chief of security if the show is centered on exploration. I think it's over done that strong female warriors are often abrasive, so lets actually make her charming and cordial. But every character needs a weakness, so why not make her weak on science and technology, at least by Trek standards. Some times she needs to get bailed out by nerdier characters. Sometimes she is able to solve problems by hitting them.
To deflect from I think of critics saying female characters are just used as eye candy. Have a female Tellarite be the chief engineer. I'm sure there are twisted furries who find a female Tellarite sexy, but I'm going to redirect an entire show just to avoid pleasing furries. I don't know if anyone is familar with
Titan AE but I liked the foul mouthed kangaroo lady mechanic. Tellarites are commonly skilled engineers and they are commonly belligerent and argumentative (but with a good reason because they believe being argumentative is actually a sign of respect). Her weakness is that she is a closet coward (not the abrasiveness because Tellarites don't see abrasiveness as a weakness). She build and unlikely friendship and they can smooth out the rough edges of the other.
I really like Quark, Garak, Neelix, Tess, Seven of Nine, and Whoopie Goldberg's character (Gayan?) providing non-Federation view points. I would have a character, probably male, probably human or human-like alien that is much older than the rest of the cast but he is not of greater rank. He joined Starfleet academy later than most cadets after having a full career as a civilian. He would show a lot of earthy wisdom and have a lot of unorthodox non-Starfleet solutions to things. Eventually it is revealed that in his old life he made some unwise deals with criminals and joined Starfleet both as penance and for protection. We could have lots of episodes as his past catches up with him.
Rene Auberjonois passed away, but I like the idea of honoring his legacy. Star Trek shapeshifters have long life spans. I like the idea that Odo is trying to steer the Great Link to make a kinder gentler Dominion.
I like Whorf as Starfleet's first Klingon. Nog as Starfleet's first Ferengi. One of the characters can be the first Starfleet Voorta or Jem'hadar.
The holographic doctor, Seven, Data, Odo, and to some extant Spock and Ezri Dax all Pinnochio subplots. A Voorta or Jem'hadar could also have Pinnochio subplots as they learn to assert themselves.
There should be a recurring or regular Caitian character because cat people are cool. I think it would be cool to show the Caitian character occasionally jumping ridiculous distances at least once. And really as long as it involves consenting adults, I bear furries no ill will. I'm not sure what crew or story role the Caitian should play. I'd say the medical officer but that mediocre-at-best animated series already created a mediocre-at-best Caitian doctor.
Again for a non-Federation perspective, I'd like to see one character be the first Cardassian in Starfleet. I'm thinking a female science officer or a male pilot. I also want to follow up on the evolution of Cardassia.
I want to follow up on Bajor as they become deeper entwined in the Federation and have a Bajoran character. The main cast is a little crowded so maybe a recurring character. Perhaps a Bajoran admiral that occasionally orders the crew to do something dangerous. Actually I like the idea of five or six episodes a Bajoran is the captain and he gets promoted to admiral for winning a great victory but also taking a somewhat debilitating injury and he ends promoting his first officer Molly O'Brien to take over his old captainancy. Or perhaps the entire season 1 can lead up to this and then Bajoran captain/admiral switches from regular cast member to recurring cast member. When Captain O'Brien begins her new career as captain during season 2, the writers can look at obvious feedback and any characters that are unsalvageable can be transferred away and any character niche this is missing can be filled with a new character.
Speaking of Bajorans, I like the idea of Molly's younger brother Yoshi O'Brien, who had a Bajoran surrogate end up becoming a human convert to worship of the prophets and occasionally getting visions from them ("The Prophets are vague, but whatever is going on,
you are at the center of it Molly!"). He could be a space hippie character to provide a dramatic foil to Molly who is more no-nonsense like her father.
Aron Eisenberg passed away, but I would honor his legacy by having a young Ferengi ensign that is aspiring to follow in the footsteps of the legendary captain Nog.
In the unlikely event I have room for one more character, I'll throw in a male Orion who joined Starfleet because he felt constrained by the Orion's glass ceiling against males (I believe Orion lore was rewritten to put females in charge with the "female slaves" being a subterfuge to fool other races)
There, I have my Star Trek crew, now I'm going to make some Earl Grey tea.