The two combat systems are the hardest to wrap your head around, even for people who have played older versions of Traveller.
I'm afraid I'm not going to be able to give you any help on that one.
A good mission for a single ex-military player might be to run a GM-ed version of the free "Into the Star" adventure from Terra/Sol games. Terra/Sol is a different setting than the standard Traveller one, but the game rules remain unchanged, so "Into the Star" can serve as inspiration. If you don't feel like tracking that one down, here's a very similar idea you could work up yourself:
You just got out of [whatever service] and are looking for some work. A friend in-system puts you in contact with a Patron who wants you to infiltrate a small base on an asteroid and retrieve some data for him. The base can be whatever you want; a rival corporation's secret lab, a criminal organization's terror cell armory, whatever works best for the "mood" you and your players like. The Patron should lend you any special equipment you will need, but you must pay for damage or loss out of your reward money.
The base itself should probably have electronic locks to hack with Computer skill, guards to defeat (either robotic or human - robots are nice because a smart player can sometimes find the control room and shut them all down), a few scientists to question/kill/kidnap, and possibly a "boss", though if this is a short adventure, the "robotic security system" itself can be the boss.
One thing to keep in mind is that Traveller combat can be pretty deadly, so make sure your player has some armor and cover to hide behind. Also make sure the enemies aren't too good - usually Weapon+1 is sufficient for standard guards.
Use Recon and Stealth checks. (It's ok not to have the skills - remember the unskilled penalty though). Especially against robots, it's probably easiest to just pick a threshold to avoid detection. Use Recon to spot security cameras (Average, Recon+Int). Sneaking past guards: Difficult, Stealth+Dex+[Effect of Recon roll]. If the player has a map of the security cameras, then I'd just give him a +2 instead of making him roll for Recon to find them. (A side note - security robots probably have all-around vision, so "sneaking up behind them" isn't really an option.)
If your player is more interested in mercantile pursuits, you could have him or her trying to either pick up or deliver a less-than-legal package, rolling against the Law Level and using Admin, Carousing, Deception and similar skills to try to avoid "Imperial Entanglements".
And Exploration minded characters might find themselves tasked with visiting a colony that hasn't reported in recently. Any old Star Trek or Forbidden Planet type scenarios could be used here.
With those suggestions out of the way, I would be remiss not to mention the Freelance Traveller site, which is chock-full of ideas.
http://www.freelancetraveller.com/features/advents/index.html will get you started.
