Start by buying a second laser for your Tarsus. Your first couple missions will be kinda tough, depending on what you do.
Run some in-sys missions. Avoid anything with definite enemy contact if you can, until you get a few upgrades. Only get into a fight if you're certain you won't end up as floating, frozen chunks of scorched meat.
Upgrade your Tarsus until you have the following items:
Afterburner
Engine upgrade
jump drive
all systems map
10 missiles (not really an upgrade, but neccessary)
better guns (eventually, you'll want twin tachyons)
Tungsten armor
Memberships to both guilds
After this, you can leave Troy and move to some other system, such as Perry, Oxford, xxn-1927, New Constantinople, New Detroit. When you get relocated, start working patrols, scouts, and attack missions until you can upgrade to a better ship. (I suggest Oxford, doing three patrols at a time).
The best loadout to have when you go for the plot is:
Centurion with
Engine Upgrade 3
Shield Generator 2
Afterburners
Rear turret w/ 2 tachyons
Tractor beam (on turret)
Missile Launcher (10 missiles)
Torpedo Launcher (or another missile launcher, if it'll let you)
Quadruple Tachyon guns
B and S Omniscient tracker system
ECM package 3
Repair droid
That's all I can remember at this point. With those items you'll have a pretty simple time running missions. In RF, upgrade those tachyons to fusion guns, get the shield regenerator, better engine and shield upgrades, advanced repair droid, gun cooler, thrust enhancer, plus whatever other items I can't remember.