Ok, this took long enough to write that others have already jumped in. I agree with everything they say, but will add a few notes of my own:
The easiest thing to do is get your group together and decide what "flavor" of scifi game you want to run. I don't recall the page number, but there's a section in the main rules (it might be called something like "skill packages") that outlines a couple of types of games, from the Firefly-like "Free Traders" sort of game to a "Mercenaries for Hire" to a "Will work for credits" type game. If you can decide this before your first gaming session, then the GM can have a better opportunity to prepare. (More on this later)
In general, Traveller games are set in "known space", and though there are frequently under-explored regions on most planets, most of the source material assumes that the planets are more or less like "Star Wars" planets - everyone knows where they are and roughly who is living there, even if many of the planets are barren wastelands with very little there but a starport/startown, a local crime family, a few farmers and some dangerous natives.
I would look up the Regina Subsector of the Spinward Marches Sector on the web - that was the old "starting" subsector from when Traveller was first written, and still has the most available information, including lots of free and cheap stuff on the web.
[You could even do an "exploring the unknown" game where your players are hired on to an exploration ship to go "where no man has gone before". In that case, you'd use the world and animal generation rules every session to come up with a new planet. This could be tough for the GM, but if you have a GM who likes inventing worlds and yearns to write episodes for "Star Trek"
, this could be a good way to go.]
Once you pick the type of game you want to run, players should roll up their characters at the same time. I personally find that I have better success when players don't just enter whatever careers they want, but come up with some way that they would all work together, like maybe some Navy and some Marines, or Scouts and Space Scientists, or whatever.
You can of course always go the "rag tag band of misfits", and use the "skill packages" to help smooth over the missing skill sets in the party. In my experience, in most "plain ol' adventure" campaigns, it pays to make sure that everyone has at least a little gun combat and vacc suit skill, even if it's just Skill-0 level proficiency. Stealth, Recon and Tactics are also important, as are the "professional" skills (Electronics, Mechanics, Engineering, Piloting, etc.), but these are generally better to have a specialist character focus on each. (One thing that might take some getting used to in Traveller - skill levels do not need to be high to be useful. Level-0 means you are competent but inexperienced, Level-1 is good enough to get a job doing that thing, and Level-2 means you have many years of experience. Higher levels push you into the realms of being notably good at something.)
Then when you have your party assembled, either roll a random Patron encounter (in the main rule book) or since this is your first time doing Traveller and SFRPGs, head over to http://www.freelancetraveller.com/features/advents/gotg/index.html and pick an adventure that sounds fun. The GM should pick an adventure before hand if you already know what sort of adventures you want to have.
You could also do a simple "infiltrate a remote outpost to retrieve some object for an employer" type mission. Terra/Sol games's "Into the Star..." freebee (look for it on RPGNow.com) could serve as a useful prototype. Though it's a solo mission, it can be used as a springboard. (You'll find that SFRPG's also have "dungeon crawl" type adventures, usually of derelict space ships or asteroid mining/research facilities. Those are often the easiest to get players involved with.) For sure, the GM should download and read the "Secret of the Ancients" free campaign. Not so much to run it (though of course you could) but for some of the setting descriptions. The first installment in particular has some good fodder for adventures.
One thing to keep in mind when running or designing an adventure - Traveller combat is deadly, and healing is not fast.
There aren't any "health packs" in standard Traveller, though it's not unreasonable to interpret the "Medical Slow Drug" as a health potion that works overnight. The rules want you to have a doctor and medical facility handy because accelerating the body's metabolism that high is dangerous, but in my games I allow any character with some medical skill and a medkit to heal up one friend per 8-hour rest period.
Because of the deadliness, I'd stick with weapons like the various pistols and carbines, and save things like assault rifles and (more importantly) plasma and gauss guns for later. Also, make sure the players have some sort of armor. Remember that a Vacc suit (space suit) is pretty good armor in a pinch, and will be the most common type of armor used on those space salvage "dungeon crawls". Otherwise, Cloth and Flak are popular and won't get you in too much trouble with the locals, though in general on a civilized world the police are going to be suspicious of someone walking around in lots of armor, even if the law level technically permits it.
Expect an armored character to get a light wound every other time they're hit on average, and be seriously wounded after 3-5 hits. Become familiar with the combat rules, and I suggest using the "if you drop an enemy to 0 End in one shot, they go unconscious" rule for sure. Let PCs and "Bosses" use the more complicated rules to stay on their feet longer. Another thing to remember is that enemies will not usually fight to the death (unless they are robots, who make great opponents - no moral qualms about "killing" them, and they usually aren't as good at shooting as people), but should consider surrendering once 1/2 of them are incapacitated.
Another idea is to focus on "stunner" weapons - no need to kill someone when you can just incapacitate them. Save real killing for missions that require it, like assassinations or mercenary gigs. But that's more of a flavor thing, and your group may not want to travel in areas where that much courtesy to your "victims" is common.
Some other ideas - since you don't have Orcs and other monsters, you can (as I've mentioned) use Security Drones and other robots for your simple "wandering monsters" type enemies, or you can introduce a hostile alien race. Or even just some run of the mill "bad guys" who have caused so much trouble that they deserve a little retribution.
But the point is, Traveller games are often as much about non-combat skills as they are about combat. Trying to save the passengers of a damaged ship in a decaying orbit can be a very exciting adventure (especially if the characters happen to BE passengers) if the GM keeps ticking off the moments with the ship's computer - "Warning, atmospheric re-entry in 10 minutes. Danger, hull integrity loss imminent...." Of course if it turns out one of the passengers is a saboteur/terrorist who does not want the ship to be rescued....
