I made my first character by doing missions and it is quite easy, if you know what you are doing. You just need to follow a few guidelines:
1) Always take missions that only require you to kill one ship or station, this way you can "grab the money and run"
2) Always upgrade to a new fighter the second you can afford it and the equipment. I'm not talking about the million credit units, I'm talking about the mid range units like what you used in SP.
3) Always select missions that are under what your ship and skill level can handle.
4) Actually READ the mission description! Need to just kill the one space station or kill everything? Will some friendly NPCs be joining you? (NPCs are a bad thing, they almost always mean more hostiles will be present)