Welcome aboard!
To address your original question: Vincent did a good job... I'll add some details for the ones I know. For the smaller ships, I put their name and then the symbol used in game.
Here's the rough description of each:
Tarsus # - Light scout ship, weak but cheap
Talon V - light combat patrol craft, very weak but packs a punch and is very agile/fast
Demon M - medium combat vessel, as fast as a talon, better protection and energy reserves, tough in a fight
Orion O - heavy combat slug.er...tank. Heaviest protection, high energy reserves, a real slugger but slow and boggy.
Centurion (solid diamond) - elite bounty hunter fighter...FAST...TOUGH...MEAN...the pinnacle of mercenary ships
Galaxy X - small merchant vessel. good balance of protection, cargo, speed
Ulysses (big asterisk) - another merchant vessel, new to me so I have no opinion
Stiletto I - confed (navy) light interceptor... weak protection but there's nothing faster or more agile
Broadsword 8 - confed heavy bomber....no afterburner, a real slugger and very well protected
Dralthi C - Kilrathi light/medium patrol fighter....very fast, good weapons, decent protection
Gothri D - Kilrathi elite heavy fighter...a formidable foe for ANYONE. Heavy guns, good missiles, thick shields and armor, fast, agile, has a rear turret...tough!
Big ships:
Paradigm - Confed destroyer, a tough opponent
Kamekh - Kilrathi corvette/light destroyer, tough
Drayman - huge merchant marine transport vessel/freighter
The others are new to me so I have no description/opinion.
In general: Keep trying....the orginal Privateer was very frustrating at first, until I figured out that the real goal is to make the best of what you have at each level. You're doing well, once you have a new ship and good upgrades a LOT of doors will open.
some key upgrades to the Tarsus:
You dont want to put gold level parts on a yugo, right? So, upgrade all the armor, always carry at least 20 repair nano-robots (they work automatically over time to chip away at damage). You should use either a meson blaster or mass driver (I'd choose the mass driver for sheer damage output/energy input factor).
Get a missile launcher with FoF missiles and use them carefully (lock up the enemy on their approach and fire off the missile when their shields are below 50%). Be careful with missiles, the engagement window is VERY narrow (look at your [e]valuate window in the upper right and watch for the lock-on count up and "LOCK" indication...if the ship jukes left or right and LOCK goes away, your missile will go out dumb)
Until you're beefed up....try to stick to safe systems and work the trade routes (ore from an asteroid to a refinery, adv fuel from a refinery to a big base like New Beijing, etc. and work some small courier/pass. missions). Watch the gossip for indications of special commodity events (ex: "Andingmen in New Beijing just opened a new seam and found tons of gems" means that gems will be very very cheap at that one base until the game engine closes the event).
Have fun!