Early on, delivery missions might seem safe, but even 'low' danger still has a pretty good chance of being ambushed at the delivery site. As the game progresses, this becomes more like 100% chance.
The ambush uses concentric rings of fighters, EMP mines, and capital ships w leech missiles. The best way to get through early on is to just put the pedal to the metal and go straight for the docking bay at the station, using booster and deflector liberally. Later, when you have a stronger ship, you can try and fight your way through... but the payment remains the same whether you just dock at the station or fight.
If you have a fast, nimble ship, dead drop missions are easy cash, as once you pick up the package and get away at the drop-off point, you are home free. Once again the payout is the same regardless of running or fighting, so it is more time-efficient to just run.