I've said on other threads that I wish Shelby had been the captain and that Ro had been on the series as well. But keeping the characters and basic premise that we got, here are some of my thoughts:
-Maquis would not be putting on Starfleet uniforms at the end of "Caretaker". It would take a season, two, or more before they put on the uniforms, and even then, it might be piecemeal and not all just one uniform decision.
-More interpersonal conflict, between Starfleet and Maquis, but also within both sides too.
-No Neelix or Kes. I'm fine with them having Delta Quadrant denizens on board, I just found Neelix very annoying as a character and Kes was sort of bland. If I kept Neelix I would've played up more his more unsavory side.
-Make the Viidians and not the Kazon the main villains in the early seasons.
-Give the series a more desperate air, where it's a more of a struggle to find resources. And we see the ship dinged up more, for longer time.
-Make Species 8472 the next major series big bads, taking out the Borg completely, or almost completely. Also, do more with the Swarm, Voth, and Vaadwaur.
-No Borg overload and no Borg children onboard.
-Keep Seska around longer, perhaps recurring or as a prisoner on Voyager.
-Have Seven of Nine's physical transformation be slower. As she reclaims her humanity we see the physical changes so we get sexpot Seven more toward the end of the series than at the end of "Scorpion Part 1".
-Like the idea I saw of a DS9/VOY crossover, so I'm pilfering that one. It would've been neat to see the crews interact and to see Voyager have to deal with the Dominion.
-I wouldn't have minded a flashback episode or two about the original Voyager crew. If I recall, the mission against the Maquis was the first for the vessel, but it didn't have to be. There could've been room there to have it where Voyager has been around for a while. I think it could've been a nice change of pace and let viewers see what the original crew was like and perhaps to see how Janeway's command style had changed. That could've also been a sneak way to do a TNG/DS9/VOY crossover as well.