I've played a lot of Privateer over the years, even on a computer without a hard drive some years ago. I've got a lot of experience with the game, so I figured I'd share my experience.

First, you're going to want to be fairly well-equipped before you leave the Troy system. You may not want to build all the way to a new ship, but it wouldn't be a bad idea.

The first thing you want to buy is a second Laser. They're cheap, have very low every drain, and a very good firing speed.

Next, work toward a second missile launcher. All of the missiles have very good striking power, and early-game when you're mostly facing Talons, two ImageRec missiles in rapid succession will generally be an instant kill.

After that, an Afterburner. This will help you get places faster, and also give you a fighting chance if you get caught off-guard.

Once you've got those, upgrades are generally personal preference. Here's how I go.

Tungsten Armor
Replace Lasers with Meson Blasters
Repair Droid (If you're patient, this will save you tons of money.)
Engine Upgrade 1
Shield Generator 2
ECM Package 3
Jump Drive

Here is where you'll want to upgrade your radar. You can either go middle-of-the-road and get a Hunter AW6i (friend/foe coloring, target lock) or go the whole hog and get a B&S Omni (full coloring, target lock, ITTS (guns lead indicator.)) I would go for the B&S Omni.

After this is when you'll start saving for your next ship. There's not a lot of money to be made doing cargo runs, so the Galaxy is not a good idea unless you want to be a pirate and kill Merchant ships for their cargo, ignoring the story missions.

The choice between an Orion and a Centurion mostly comes down to the question, "Would I rather be able to burn enemies down in rapid succession, or would I rather have a slower, but extremely durable ship?" I've never built an Orion myself, so I'll cover the Centurion. I recommend you aim to have at least 200,000 credits left over after selling your Tarsus. That'll get you everything I'm about to list.

In order of priority:
4 Meson Blasters (10,000)
Tungsten Armor (1,500)
Engine Upgrade 3 (60,000)
Shield Generator 3 (50,000)
Afterburner (3,000)
Repair Droid (30,000)
2 Missile Launchers (20,000)
ECM Package 3 (15,000)
Tail Turret (2 Lasers, Tractor Beam) (19,500)

Once you've got all this, work toward replacing your Meson Blasters with Tachyon Cannons, which are comparable in every field except damage, where they outperform Mesons by about 56%.

If you want to get a Centurion earlier, you can equip one pretty well for about 100,000 credits. Here's that build.

4 Lasers (4,000)
Tungsten Armor (1,500)
Afterburner (3,000)
Engine Upgrade 3 (60,000)
Shield Generator 2 (30,000)

I recommend waiting for the full build I posted, so you don't lose money swapping components.

Anyway, once you've got what you want, you're ready to do the story missions. I've actually made it as far as the Palan missions in a Galaxy, but then got torn to pieces over and over and over.

And yes, I am aware of the recommendation in the manual to always have a higher level of engine than shield, but I discard that for the simple reason that you can always lower your shield output.

VERY useful PAL (Thumbs up) ... it changes totally my way of playing, i was frustrated by spend so much money and long battle with stupid lasers... now 2 IR missiles in a row, POUM! 1 ship, other 2 missiles, POUM! other ship...

Fast killing to go to the story, i suppose the second ship i can buy with patience it´s the Centurion right? I wanna play focusing in the story mode.