Each of the ships in Wipeout HD is balanced differently. There are some that are clearly inferior (ie, the overall total of their stats is lower than other ships) but they balance that by having best-in-class performance in a certain area. Depending on the track, they might outperform a ship with overall better stats, simply because they focus on an area important to the track.
Your play style (and strengths/weaknesses) factor into this as well. If you're good in a straight shot, but terrible in turns, you may want to pick a ship with better handling, for instance.
This guide lists all of the ships and their respective stats (including the unlockable ships) so that you can determine which one you like best.
The Fury expansion pack unlocked a new set of ships with better stats - these ships are categorically better than their 'standard' variants. There's no reason to use the 'standard' ships if you have the Fury expansion.
Skins are unlocked for completing certain challenges, and they factor into achievements, but there's not much else that they do besides that and showing off your Wipeout HD skills to other players online..