Quint; how would you administer 2001 as an adventure?
Ok, @Hemdian did a good job of answering this but I'll add in my own take. First off, this really has two good potentials - as a campaign/setting in and off itself or as a strong storyline within an existing campaign. I've actually done this a couple of times over the years, plucking the various elements that I wanted to use at the time.
Personally, to closely replicate the movie, I would start with the TMA-1 section (the second section of the movie, on Luna). Characters can either be experts pulled in to the story post-discovery like the movie (and the witness or spark the transmission) or they could be the people who discover the monolith in the first place and then continue through the rest of the adventure.
Then it moves to the Jupiter mission (the third section of the movie) and this is mostly kind of classic Traveller (small crew, insane AI, mysterious object to be investigated). This whole section can run pretty close to the storyline of the movie IMO.
Finally, after the secret has been penetrated it moves to the final section of the movie (Beyond the Infinite) which I think could also easily include a section that duplicates the first section (Dawn of Man).
A lead in to the events of 2010 is pretty easy as well, with ether ignoring the whole "Cold War" piece or translating that to tensions between the Imperium and the Consulate/Confederation/etc. Cue huge showdown between fleets as the players are stuck trying to escape the about to change gas giant. Characters can be revealed to be spies for whomever, etc. Much of the flavor of that film can be retained if wished.
For a game, one of the characters could certainly be picked as the Starchild and then be retired, but it could also be a gestalt of the groups mind as well. Cue psionic awakening, cue special psion abilities when together as a group, cue... you get the picture.
If the goal is to use one core group of characters for the whole set of adventures then I'd make them field scientists for the most part with the "right sort of focus". I've used the Ancient's Foundation IMTU as a nice proxy for this sort of campaign. It also gives them the potential authority to basically take over or run the investigation.
You could also run this simply as "Free Trader crew" whatever, and place it in an isolated system with either a low tech or extinct race where they stumble over things initially as a fluke (or simply because they are scanning for resources and discover the monolith on the moon).
Note that the long periods of time between sections two and three of the movie is due to TL8 standards of the movie. Move this into the OTO or an close analog and things move pretty much as quickly as the GM wants them to.
Hope this answers the question!
D.