Even in TNG's era, it still took hours for a transmission to reach a ship. (See "The Defector")
As for a reboot, cast actors appropriate for their station in life. Captain Kirk was an experienced officer who took command of the
Enterprise after a stint as a destroyer-class ship captain. Thinking about that, why not start the first film with him commanding this ship and showing him on the path to commanding the
Enterprise? It was constantly repeated in the first series that commanding a starship class vessel represented the pinnacle of an officer's career. Commodore Stone says, in "Court Martial",
Not one man in a million could do what you and I have done. Command a starship. A hundred decisions a day, hundreds of lives staked on you making every one of them right.
The Next Generation brings up something that I feel isn't explored in Star Trek often.
Data, "The Last Outpost"
They should add also that Starfleet has refused to prevent several civilizations from falling; we have sometimes let the violent and the strong to overcome the weak...
Finn, "The High Ground"
Captain, there's a lot to admire in the Federation, but there's a hint of moral cowardice in your dealings with non-aligned planets. You do business with a government that's crushing us. And then say you aren't involved. But of course you are. You just don't want to get dirty.
These two quotes are still topical today, for we see this constantly happening in international diplomacy. I think we see this in what is happening in the Middle East.
I am not capable of writing a story, but I would hire a writer who can do a script that balances action with diplomacy and exploration, and depicts how Kirk manages to solve a crisis with the above quotes as a foundation for that crisis, and how that situation impresses Starfleet to think of him as the right man for a starship command. There are ways I can think of how I would introduce Kirk to Spock and McCoy. I would look to history, for there are instances where similar situations occurred, as inspiration. And, I would be encouraging a story that is strong on science and weak on supernatural phenomena.
As for the other characters, the question is, who is essential to Star Trek? I would keep Scotty for sure. I have always felt that he was important after the trio. Then Sulu, possibly. Uhuru and Chekov are dispensable characters. I have seen another man who rebooted the franchise who elected to forgo a character that some consider important. I am speaking here about Nolan and the Batman franchise and Robin. I think this is important question to answer, for it has been proven in the Star Trek films that in a large ensemble piece that a large number of characters have been slighted. Concentrate on the core, bring in those characters who add to the core, and drop those who don't add to the core.
