This game pretty much WAS a lot of my childhood. It's a side entry in the series canon, taking place at roughly the same time as Wing Commander 2: Vengeance of the Kilrathi (2669 CE.)
There is a storyline woven through the game; a TAS would aim to clear through that storyline, as otherwise you can just do anything you want. There's a description of the story missions in
this FAQ, starting from part 12.
If I recall correctly, the only parts of the game that involve heavy combat are the missions in Palan (blockade breaking, lots of mercenaries) and the missions for the Exploratory Service (unclaimed territory, lots of Kilrathi and Retros.)
You can take up to 3 missions at a time; most remain available to complete until you do them, with the exception of cargo missions, which once you take off must be completed by the cargo's destination being the next place you land (so you can't do cargo runs to multiple locations.)
Ideally, a TAS would use some combination of luck manipulation and strategic use of accepting missions, then saving and reloading the save (which refreshes the mission lists) to take cargo missions going to the same location a plot mission is going, and/or bounty hunting missions with the target being either along the way to a plot mission system, or in that system. (The best-paying bounty missions have the target in one of 3 connected systems; I don't yet know when the location of the target is set. I think it's set either when you accept the mission or when you launch for space.)
In basic Privateer, the Tarsus-class ship you start with is utter garbage for combat in the later stages of the game, due to its' low capacity for reactor and shield upgrades, not to mention it's slow. The Centurion-class heavy fighter is the most expensive ship you can buy (200,000 credits) but luck manipulation like I suggested above can get you into the cockpit of one pretty quickly. The question then becomes whether to grind for money before starting the storyline, and how much of that (if any) you should do. My personal opinion is that you should wind up in a Centurion around the Palan missions, which as I mentioned are fairly heavy on combat.
In the early game, the Tarsus will work out okay once you have enough for a second missile launcher; rapid-firing 2 IR missiles (ImageRecognition) will quickly destroy most fighter-size ships except Kilrathi ships, and those are rare in the area where you start the game.