Like I mentioned earlier, before you set out it might be a good idea to earn some extra money doing other things to build up your ship a bit. The demo is limited in this regard, but the full game has a lot more planets and I think better balanced mission rewards. A good strategy is, if possible, get behind the larger ships and pound away and be sure to pick up their cargo once you destroy them. Remember to repair the damage cargo items before applying them to your ship or selling them.
Since you didn't pick up any illegal cargo that you know of (most common friendly-fire reason), it might be that you've accidently struck the starbase or one of the surrounding satellites with a weapon hit. If it's just once, I think you can just move outside of their weapons range and then back and it should be ok, or quickly dock at the station - I think that works too but I don't often hit friendlies by mistake.
