Run Death Station for your group - it is a free adventure you can find in a few places.
It is a great introductory adventure and here is the one change I would make, ignore the big bad in the adventure and instead have the Station taken over by samples that are being studied that were obtained from a wreck in the Great Rift...
I can go into more detail if needed.
This gets the players involved with the entity, now for the fun bit, they can also on the Death Station find the memory/personality recordings of the group that found the derelict in the Great Rift, that gives you the opportunity to run that adventure as a flashback, simulation, VR, whatever.
Great Rift Adventure 2: Deepnight Endeavour Great Rift Adventure 2: Deepnight Endeavour takes place aboard a derelict exploration vessel which the Travellers must enter to locate fuel. With no way to get home, they discover there are survivors, and that t
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They can then be signed onto the Deepnight as a follow up to Death Station, they are now experts of a sort now
As to running DR from start to finish just go for it, it is no more difficult that Masks of Nyarlathotep, just do it one adventure at a time...
Come back and read what others have said about the campaign, I think it is the second best Traveller campaign there is, only Singularity beats it.
The only issue with it is it is very expensive to get all the add on adventures that go with the core campaign, but they add so much to the campain I consider them well worth the investment, if only in the pdfs.