It's a lingering question in Star Trek mythos: Kirk or Picard. Now, I despise fanboyish "If X would beat Y" matchups. Such things quickly break down to become intellectually bereft contests of popularity and nostalgia, backed up with arbitrary points of canon married with tenuous 'logic' to back them up.
I'd much rather explore a crew for a Star Trek show that utilized characters who have enough character to be interesting, but never got enough exploration in their actual appearances. A television show or series which got to develop under-used characters--however irrelevant it may seem in the wake of the new Trek movies--is certainly more interesting.
The first step is to establish a ship, a mission, and, a series. These are, after all, characters in a story...but what story? The Star Treks franchise thus far has given us a peek into real scientific theory and what it could mean for mankind, a bright future where the human spirit--not technology--elevates us above our state today, truisms about human nature and politics presented honestly without familiar context, and stories that try to hit one or more of those points and fail embarrassingly. DS9 did it's own thing to become a serial drama, and in that respect did very well, but being a serial drama about flawed humans might make it good television and very enjoyable science fiction, but sadly, it doesn't make it good Star Trek. Voyager, for its many, many, many flaws is actually a very good example--in terms of format--of narratively disconnected episodes that keep a consistent overall theme.
I'm not thinking of doing anything new here. I'm mixing and regurgitating Treks to make a franken-series. We're in the future, we're on a type ship we've seen before, we're dealing with alien races. Tone is paramount. Worf was a waste on TNG, but shined in DS9. Or could you imagine Kirk spending an hour alone with Troi and talking about his damned feelings? Janeway during the Dominion War? Setting can make or break some characters.
I'd like a series that can occasionally be a vehicle for both social commentary and the newest science available to us. I don't mean comic book newest science that makes the plot go, but elements that show us the impact that new scientific discoveries imply about the universe at large. The driving force that solves problems should be humanity, reason, and hard work.
Mission: I think that a good format would be something akin to The Next Generation; mostly exploration, but also a handful of diplomatic and scientific missions. TNG is quite possibly the most beloved Star Trek because it left itself open to do a lot of things that weren't metaplot related. Sure, DS9 and Voyager both swam against the current a bit, but they were still in a river headed one direction.
Theme: Star Trek has always had a theme of danger, exploration, and camaraderie. Danger delivers a certain amount of requisite, narrative heft. Exploration is the driving force for these characters to do what they do despite the dangers. Camaraderie in inherent to the human element; one part of showing how the human spirit can overcome the problems is for people to work together. Not always well or perfectly, but still together.
Story: There are not a great number of smaller powers in the Star Trek Universe. Generally, it's just Ferengi, Romulans, Klingons, etc. I'm thinking a confederation of planets that isn't the Federation. There are certainly complaints to be lodged against the Federation and the way they do things (So'na, Maquis, Prime Directive, Dominion War, Section 31, etc.). This "Trek" would consist of a handful of ships, secondhand from Starfleet, the Federation, or whoever is selling starships this week.
Mission: To patrol the border, coordinate diplomacy and joint operations with neighboring states, capture pirates and smugglers, explore new tracts of unexplored space, either as survey and first contact, or simply providing an accounting of territories.
Ship: I think my crew wouldn't have the biggest, bestest, boldest, or
biotechist ship in the fleet. I'd opt for a Nebula Class; modular
starship with a visual look similar to that of the familiar Enterprise-D.
Mood: This star fleet doesn't carry over the strictness of the Federation, but they're still professionals, and they're still a team. A 'young nation' feel prevails; they don't have the staid demeanor of The Federation; they don't have a rulebook, instead opting for a common ethos. While the captain does have the option of how to deal with issues, explaining his/her reasoning to his/her superiors when things go wrong is an essential element.
Billets: Just which stations a ship needs 'named' characters for is a relevant question. I don't need the expansive cast of DS9, and since I don't need to shoehorn in Worf or a second Dax, I can skip over Strategic Operations Officer and counselor.
Captain: Someone in the commander/captain area. He/she's most of the authority for the ship and often takes an active hand in the ship's operations.
Second in command/other billet: With a smaller, crew there isn't the extra space for full-time middle-management. Like with TOS, the number two will do something useful on the side.
Engineering: Who can fix an engine with bailing wire and duct tape better? I could settle this one here, easily, but for the sake of consistency, I'll cover this later with the rest.
Tactical Operations: In tactical, you need someone perceptive, quick, and possessing, above all else, good judgment. A captain may not have time to order the shields raised or to order torpedoes fired, but a good tactical officer knows.
Security/Operations: I wrapped these two together instead of the more classic Tactical/Security combo established with Worf and continued with Tuvok. I get where you have a 'combat guy,' but I don't see where using the shields and hunting down boarding parties are the same damned thing. Given the coordination that has to happen between the Helm, Security, and the Captain, it's pretty amazing anything happens on a starship ever, but then, that's really the Enterprise, which--despite the fiction--handles like a fat guy running serpentine uphill. Maybe timing isn't that critical. Anyway, the position calls for someone with a good spine and an excellent head on their shoulders. Someone who has a good grasp on overall ship's systems and knows how to catch a thief.
Navigation/Helm: The guy who pilots the ship, and I guess plots courses. It's sort of a standard position, but one that's something of a red-headed stepchild. I mean, our most prominent helmsman was Tom Paris, who was diet Will Riker, who was, in turn, diet Jim Kirk, so that makes him something like half-and-half tap water with store-brand cola. Try some of that. It tastes like barf mixed with coffee and industrial runoff. That's Tom Paris.
Sensors/Science: These come together pretty well. It has always amazed me that only the original Enterprise and DS9 had a science officer. But then, even DS9 phased theirs out. The rest had ill-defined, engineer/scientist/borg/Janeway officers to solve their crazy puzzles. I'd like to have someone back at that post.
CMO: I want a doctor who isn't preachy or holographic. That's setting the bar pretty low. I think we all know what makes a good doctor.
Non-Crew Dude: Y'know, the guy who isn't one of the guys. Guinan, Neelix, half the cast of Deep Space Nine.
Next Week: Decidination