Hi Andrius, welcome
You can find a list of the starting ships and other usefull tips in
this thread.
Here is what it says:
The starting ships are Wolf, Lasher, Vigilance, Hound or the Shuttle. The re-start (if you die) ships are Shuttle/Dram/Hound. Which Ship you get depends on the second choice you make for your characters personal history.
The Wolf (choose 'quartermaster') is often considered the most powerful of the starting ships, but is hard to control. It has initially no PD, a somewhat temperamental shipsystem, and struggles against shielded foes due to its reliance on beams.
The Lasher ('adjutant in the Hegemony Navy') is much more newbie-friendly. It comes with three PD weapons, an easy to figure out system, and has the most flexible mount type (there's a ballistic weapon for nearly every role).
The Vigilance ('helmed a patrol ship') is also a good choice given the right initial skill choices and weapon loadout, but again, probably not something a newbie will be able to figure out.
The Hound ('something else') should be avoided unless you put your initial skill points into unlocking the Frontal Shield Generator hullmod. The first thing you'll want to do is get a wing of Talons to increase your survivability slightly.
The Shuttle (always a choice) is a 'just in case' ship - it says so right in the code - and outside of a bug with a custom character creation plugin, I would only imagine it being used for self-imposed challenges.