How to unlock ingame ships?

If I remember correctly: Once you unlock them as a starting ship they are unlocked in the reinforcements as well. So you need to reach that level.

Well it seams that the starting ships are not the same as the reinforcement ships (I cannot buy ingame the same ship I started with - flagship). 
So my question would be: is there a wiki link somewhere to see what are the requirements for unlocking reinforcement ships?