I second the "keep it local" sentiment. What sort of style are you going for? If you're running a heavy military game your players need to know different things than if you're running one centered around trade or psionics.
My Third Imperium 101 list consists of:
- Psionics are bad and banned. They can READ YOUR MIND. Nothing is private. The Zhodani will reprogram you and wipe your memory if they catch you. This is why we must watch them. (Yes, there's a fair amount of propaganda in there for a reason.)
- Memorizing all the worlds you'll be traveling to is generally a waste of time, unless you're into that kind of thing. The ship's computer has information on local flavour and hot spots, which is all you really need to know.
- The Imperial Navy means security. They also mean business. Keep all your papers and documentation in order, preferably in triplicate.
- Some planets are less stable than others. Be nice to strangers, you never know who has PTSD and is in the middle of a really bad day. (I tend to play around the Darrian/Sword Worlds border. This point may not apply to your game.)
- Aliens exist. Most of the ones in the Marches are cool, but don't ever pick a fight with an Aslan or Vargr.
- You can get more cargo. You can't get another life.
- Always assume the other ship is faster and better armed. Always.
That's the general gist of it, and I generally pass it along through NPCs. Really, the players don't need to know *that* much - how many people can name the current finance minister? Political apathy exists in the 3I just as it does in the real world.