If two ships are the same speed, then who goes first is a coin flip.
If the fastest ship on each side is not the same speed as the other, then the fastest ship goes first.
Speed increases with the GP rating of the ship, which increases with Stars, Level, Ability Increases, and Pilot/Crew GP.
If your ship is 5 stars and you're facing an enemy with a 6-star version of Punishing 1, then you're very probably going to have a lower speed and always go 2nd. (Of course, if you take Dengar to r9 or whatever, you might be able to overcome your star disadvantage and get the higher ship speed.)
You can look at ship stats the same way you look at your character stats to see the exact speed of each ship if you're curious.
As for stealth, it has to do with how this ability is coded:
Whenever an enemy gains Stealth, dispel it, inflict Breach on themselves for 1 turn, which can't be resisted, and Punishing One Stealths for 1 turn.
For whatever reason -- and I'm not sure why -- this doesn't appear to kick in until P1's first turn. Which means that whichever P1 goes first gets to keep stealth but dispel it on the enemy P1 & XB (if XB is present). I'm not saying that this is correct according to the kits, but it does seem to be how it is working.
Hope this has helped.
