Im just setting up for my first ST campain (I've been both a ST and a RPG fan a long time, but you couldn't get a ST RPG in Sweden until recently) but I have two ideas to choose from:
1)
The crew is composed of rouges and renegades that are thrown together when the space station they are on are attacked. It is a classic frame-tale where the crew zooms around the quadrants seedier sectors looking for the kidnapped daughter of one of the crew, while at the same tiome dodging those who attacked the station. The theme of the series will be differences in ethics. The feel will be one of not beeing adequate, a voyeur in a universe which doesn't care one bit about the characters. Outsiders.
2)
Set in the pre-ENT era, the crew are the crew of a boomer that comes a little off course. Very low-tech (no phasers, replicators, transporters). The theme would be evolution of ethics and ethics in the face of low resources. The feel will be very frontier, loneliness, difficulties, friction.
What should I pick? From which could I get the most? What will entertain the players more? How should I develop the concepts?
Players should always have a say because what kills a game is palyer apathy and they will get apathetic if they are playing a game they don't really like.
The best way to pick a game if the players cede the choice to you is to think about each player individually and see what he/she likes or dislikes. Then look for a commanlity between all the players and go with the game setting that they will all enjoy.
Of your two ideas, idea 2) may not appeal to most Trek fan/players because all the usual sthicks are not there. They're use to having transporters, phasers and replicators so if you take them all away, it just becomes another sci-fi game, not Trek. Trek is about the environment and atmosphere (partially) so if I had a choice I'd go with idea 1).
I enyoy a special relationship with my players, believe me.
For me, ST has always been about morals and ethics, not about phasers, transporters and replicators. This is something I'll impose on my players and I know they don't mind- we discussed how much better it would have been if ENT would have stuck with plasma pistols/rifles and plasma cannons. It would have given the series much more of an individual feel as opposed to just another TNG. (Which, of course is impossible, Bakula can in no way math Stewart)