Yea, the randomness is a big part of what makes this game so special. This is the only game I've played where going to the damn store will elevate my pulse.
Right now, I'm finding 4/5 play throughs I can get to the boss, that 5th game I feel like I get unlucky and I get bad rolls. I should be mad, but it just makes the rest of the game work so damn well. The ability for a few bad events, or a poorly designed system is what lends the game much of it's tension, and it's power to be so addicting. So far, I'm finding the balance between luck and skill to be pretty spot on.
Still, you can do lots to mitigate the need for luck. Every ship should be able to breeze through the first two sections, and most can slug it out in the third. Hit every node, and every shop, and i'd estimate you have a 90% chance of finding something good. If you don't find good weapons, you'll have found good crew, so go buy a teleporter and you can win fights that way.
Try not to spend any scrap in the first three zones unless you see a great weapon after that, plow cash into engines, shield/defensive stuff. if you can spare it, pick up a cloaking device ASAP, that way you can dodge missiles, save scrap, and reduce the danger in combat.
Still having trouble? Roll with the Engi ship, the ion cannon is probably the best weapon in the game, just point it at their shields and autofire. Or try the zoltan ship, the zoltan shield can eat damage and protect your precious hull, and the halberd beam alone is enough to take you through the third sector, find an ion cannon or burst laser and that's it, you've got enough firepower for the rest of the game.