From
https://en.wikipedia.org/wiki/Star_T...arch_for_Spock
Star Trek II, III, and IV make a pretty good trilogy. If you haven't seen them, I'd recommend them. I don't think you'd really need to know much about Star Trek to grasp the basic plot and be able to enjoy the movies. Um, basically in the far future earth has joined an interstellar alliance of planets called the Federation. Starfleet is the Federation's military and exploration arm, with a naval type command structure. Our heroes are the crew of the Starship Enterprise (Which operates a lot like a naval vessel or a submarine- in space). By Star Trek II, they've served together for many years and become friends.
Oh, and Khan was a genetically engineered dude from a war in 1996 (The Eugenics War- didn't actually happen, obviously, but that date was established on a TV episode that aired in the 1960s) that they found in stasis on a sleeper ship like 20 years prior to Star Trek II (He had been trying to escape earth with some of his close allies after his side lost the war)- because he was a war criminal, and tried to take over the Enterprise to reestablish his empire, they left his people on what at the time was a tropical planet, with no technology, and sort of said "Okay, you can live out your lives here and build a society in isolation". From the title of Star Trek II, you can tell that he'll enter into that film at some point.
As Star Trek II opens, we see a smaller starship (Not the Enterprise), with a former Enterprise crewmember named Chekov who had transferred over to it and been promoted, exploring a lifeless desert planet that is not what it seems.
You're basically good at that point. The movies tell you everything else you need to know- and probably some of the above, to be honest. They were made for general audiences, not just pre-existing Star Trek fans.
A lot of people consider Star Trek II the best of the movies. It's kind of a Hunt for Red October in space. My personal favorite is Star Trek IV, where they have to go back in time and find some whales to save the earth (Long story, the film explains it), which have gone extinct in the future, and wind up hilariously not blending in well at all with 1980s America.
Anyway, the three films basically form a trilogy. Star Trek III is the one that's most relevant to what we're talking about, but probably the weakest link in the trilogy as a movie (Although, it's still very good in my book).