I'd go with something in either a high-stakes diplomatic or espionage mission vein, myself. Spin a subplot or two for the characters that link in with the main plot -- give 'em some kind of teaser that gives 'em a real BAM! kind-of "action & this is why your character is such & such a way" beginning.
Choose a main character! Someone who is central to the plot and make at least one or two of the others connected to him/her in some way, to give them motivation & not leave them out. Have one character that has some knd of cross purpose requiring them to have a struggle of conscience or some such.
For the TOS/TMP era, do something with the Klingons.
If post movie, pre-TNG, use the Cardies (when they're still something of a mystery...)
If TNG/DS9 or after, I'd use the Rommies as the bad guys.
But that's just me.
"War is an ugly thing but not the ugliest of things; the decayed and degraded state of moral and patriotic feelings which thinks that nothing is worth war is much worse. A man who has nothing for which he is willing to fight, nothing which is more important than his own personal safety, is a miserable creature and has no chance of being free unless made and kept so by the exertions of better men than himself."
John Stuart Mill