If you have only three ships, you've messed up. There should have been a mission to go recover some damaged hulls; start a new game and take -all- of them. (Okay, you can skip the tanker if you want; it's not combat-useful.)
You may also want to consider: taking the accelerated start option with the Hammerhead; it comes with rare weapons and some high-value hull mods that you can't otherwise have access to at that point in the game.
Also, if you're not playing on easy, you probably should; Starsector has a steep learning curve, and while us veterans are okay on 'normal', it should be approached as more of a hard-mode than anything else.