Hello,
I'm having a lot of trouble of how to start being successful. There are so many good reviews about Privateer so I had to try the game for myself. I've read the manual, looked online for faqs, and also have looked through the forum about how to play.

With this, I'm still stuck. I dont know what to do to complete my first mission.

This is what I've done that was recommended: sold everything besides my shields, purchased afterburners and upgraded my armor to the highest one.

I've taken scouting missions and I cant put enough distance between who ever is following me so I can autopilot to safety. I always stay at 5,000-4,400 km away from the enemy.

Am I doing something wrong? Or what should I do differently?

Sincerely selling everything but the afterburner and shields wasn't a wise choice, while you could have sold the missile launcher and the missile easily I would never advice to sell the lasers because as you noticed there are enemies fast enough to tail you even with the afterburner.
Best way is have patience and remain in the starting system until you can upgrade weapons a bit, upgrade generators, etc.
Also, get a friend or foe targeting computer whenever you can, otherwise it might be too easy to hit some system patrol craft during a scuffle with retros or pirates.
Put enough away to buy a new ship, personally I'd go with the Orion first, the galaxy is basically a trading-only craft, while the centurion is mostly for combat, the Orion is a bit in the middle but it has more upgrades than both which is useful especially if you later continue into the expansion as new exclusive upgrades for it become available.

Take also into account that you can get to places without the autopilot, it's slow but doable, I was forced to retreat this way a couple of times in my early game with enemies that were always slightly behind me.

Also, save every time you can and in different slots.


PS: even when you can start adventuring beyond the starting system I advice you to always stay around the Junction System, New Constantinople and New Detroit, the more remote parts of the quadrants are dangerous and usually full of Kilrathi that will make short work of you.
Same for the storyline, don't start it until you upgrade your Orion or Centurion fully and in general took confidence with the game.