The next series needs to continue the prime timeline from after the 09 movie.
Follow the established events in that movie. Romulus is destroyed. The Romulus people are leaderless and infighting amongst the surviving empire planets and military lead the Klingons to strike while the Romulus are weak. This would cause a rift between the federation and the Klingons because the federation would be rendering aid to the Romulans.
The series should run like DS9. Episodic where the majority of the episodes story is completed in the episode, but it ties in with a larger story arc.
Obviously the 1st episode will be expensive as it will require building of the major sets, props, ect and cgi work for ships (though I prefer model work).
I don't think the show should be special effects heavy. It needs to be story driven. Special effects should only be used to help tell the story. They don't need to be the story.
Please, please, please no over use of interpersonal drama. I absolutely hated SGU. Sure there will disagreements, but they should be at a minimum between the main cast. Bring in outside characters for that, like Cmdr. Maddox or Captain Jellico.
Having main cast members that the viewers hate makes viewers not watch.
Crew diversity is fine, but for cost reasons the vast majority have to be human, and its been stated that humans make up the majority of the federation.
Also, the aliens shown do usually have vast differences, it's just that the ones in Starfleet are mostly like humans because they've all gone through training and if they acted vastly different from their crew mates they won't be around for long.