I find it hard to believe that this game is all about luck because I win most of my games, and most that I lose I know what I did wrong.
First of all, the Kestrel has almost no luck involved with winning. Your starting weapon systems could take out a four shield ship with a lot of luck, and most anything else without too much trouble. On top of that you can transition into pretty much any strategy with the Kestrel, so you know you can use what you find in shops.
SOME of the unlockable ships have a strong element of luck, but with good strategy you should be able to get a decent ship together within a few sectors. The main issue with these ships is that they start with a deficiency in some area (offense, defense, crew) that forces you to spend scrap and find equipment to overcome. There are also some ways to get screwed easily with these ships: beam drones for sheildless ships, auto-ships for boarders, and certain shop setups for Engi B. Within the first few sectors these problems should be gone, or at least you should have had an opportunity to deal with them.
There are two big rules to overcoming luck in FTL: work with what you have, and stay ahead of the power curve. You aren't trying to build the best ship possible, you're trying to live to beat the flagship. Forget making an optimal setup, if your weapon systems aren't good enough then a crappy gun now is better than an efficient gun later. This means you need to figure out what specifically your ship needs, especially in the short term. I could probably go on for pages about this but you're just going to have to learn through experience.
Learn how the power curve works, and learn where you sit on it. If your ship is more powerful than the average enemy you'll rake in scrap, if it's weaker you'll have a harder time getting scrap and your disadvantage will grow. If you find yourself constantly running that means you've fallen behind the curve and running in that situation is a terrible strategy. Remember: if you can't beat the enemies now, you won't be able to beat the enemies in the next sector. This means, oddly enough, switching to a high risk strategy. You NEED to get to a point where you can beat the local enemies, and if that means running your fuel and your hull down to the red so that you have enough scrap to get vital upgrades, so be it. You may want to take calculated risks like choosing events that could cause you to lose crew. Don't avoid fights in this situation, you need the scrap.
If you're on top of the power curve, things are much different. You have some leeway and should avoid events that could devastate your ship (such as crew loss or picking a fight with an enemy that you know will kick the shit out of you). Focus on maintaining your advantage; "scrap multiplier" systems such as the teleporter and recovery arms are a good idea. Make a wishlist of things you need to beat the flagship; for most ships its surprisingly short (for example, a Kestrel could likely win with no purchases besides an incendiary bomb and a cloak). Be aware of any gaps in your ship's systems, such as missile defense or shield piercing, and deal with them. Keep your temporary resources at decent levels but remember that if you're doing well repairs, supplies, and crew will mostly be maintained by events.