It should go without saying, but interesting characters are the key. The best TV shows (BSG, The Wire, The Shield) knew how to do great character work. It's not just giving your main characters progressive arcs, but it's also building an interesting supporting cast. That's often where Trek has fallen short. They've favored huge regular casts where almost none of the characters get real depth (Enterprise and Voyager, I'm looking at you), they lacked good supporting characters (TNG and Original series), or both (Voyager).
Trek creator Gene Roddenberry allegedly was pretty picky about which flaws and foibles his heroes could show, given that the Federation is pretty much a utopia. Captain Picard said that humanity has moved beyond greed and is pretty much interested only in enlightened pursuits, like charting gas giants and using the Holodeck to recreate 17th century sailing ships. The trick is to strike a balance. Humanity as a whole should be doing much better than us, with poverty and racism pretty much wiped out by the 23rd century, much less the 24th and 25th. But individual humans should still have their flaws.
But humanity's just the beginning. Since Mr. Spock, we've had aliens as main characters. Most of the series have been human heavy, with a couple of non-human regulars (who often look human, IE, the EMH on Voyager and Troi on TNG) sprinkled in. I say, f that noise. Build on the various aliens we've seen. Why not have an Andorian Captain? A Vulcan who doesn't share the same Vulcan mono-culture that we've seen in 5 series and 11 movies? Aliens who, by virtue of living in the Federation, aren't all that alien?
So here's what I picture. 5 or so regular cast members. A BUNCH of supporting characters that pop up in a goodly number of episodes, but not all the time. If you have a story to tell with them, great, use them in as many episodes as you want. If you don't have any thing to do with them, just don't use them for a while. Instead of having filler episodes where we watch Geordi try to fuck a hologram, maybe just let him sit out this week, and have LeVar shoot an extra episode or two of Reading Rainbow.