Every mission out, especially early on, should involve as many paying missions as you feel comfortable tackling (make sure they TELL YOU WHICH HOSTILES you'll be fighting - kilrathi are rare in Troy, but they do pop in occasionally) and a cargo run of some kind. Every trip should generate enough profit to buy the next item on your upgrades wish list (minus cost of emergency repairs if something goes pear-shaped).
Remember that in an early Tarsus, you'll be dead meat for a Kilrathi *anything*
Upgrades should go something like this:
afterburner
tungsten armor
two meson blasters
ECM1
generator upgrade 1
two missile launchers (w/ Pilum FF missiles, if you can afford it)
two tachyon cannons
repair droid
ECM 2
Jump Drive (once you have the Jump Drive, foes get much harder)
The two missile launchers will be essential! Facing Talons (retros and pirates), you can kill some percentage of Talons with just two IFF missiles. The trick is to fire at about 5000 meters and double tap the fire button - that is, hit the enter button twice, rapidly - to fire them VERY close together. If they both hit the same quadrant at the same time, you either kill the talon or need only a laser bolt or two to finish him off. Facing Kilrathi, the two missiles will either knock the shields down to nothing/1 bar (Gothri) or blast through the shields and turn the hull red (Dralthi).
It changes your game from being prey to behing a predator. You can start performing 3 patrol missions (if you can find them) and making 22000 or 25000 credits PER FLIGHT. The twin tachyon cannons give you staying power against heavy fighters (centurions, demons, gothri, broadswords) and mean that you can gun down Talons in about 6 double-hits.
A Tarsus with the above upgrades is about the most ferocious thing you can have, IMHO, until you earn enough money (~300,000) to afford the jump all the way up to a Centurion with 2 lasers, 2 tachyon cannons, two missile launchers, Generator 3, Shield 2, tungsten armor, turret with tractor beam, ECM3, etc.
Anyways, have phun! ;-)