I've played like 10 and I can't say anything sticks out! But it's a very random game and I have been dreadfully bad at it. (It's REALLY HARD now... on Normal.)
And there is a hard mode now :D
Well there are little tricks to know that can help you improve dramatically and that was valid before the expansion. Stuff like prioritising a second level of shield in the first sector will help through encounters in the second and third sectors, but don't buy it ASAP as you may find a store with a good item in the first sector; if you got the crew for it, having a teleporter or cloak at the start can be a great help and it's better to keep your scrap for something that will help you immensely than spending it as soon as you got it. After all you can upgrade your ship pretty much anytime but stores are more infrequent.
Speaking of scrap, you probably know this already but you do not want to spend it too much on repairs. If you do then you can't spend it on upgrades and eaquipment, meaning you'll take more damage, meaning you'll need to spend more scrap on repairs that you won't spend on upgrades, etc. I often go low on damage in the early sectors as I can easily find ways to mitigate it (second level of shields) and that means I may be able to buy a good weapon or piece of equipment that will let me turn the situation around by sector 3 or 4 by making encouters easier and thus providing more scrap. Speaking of buying, crew is usually a poor purchase option unless you have a special need; the game usually gives you many opportunities to gain crew through various events and encounters.
Doors level 2 is a pretty good upgrade and very cheap. It lets you deal with fires and boarders easier while letting the rest of the crew operate the ship. Some say you should get it ASAP but I disagree and prefer to keep scrap for a second layer of shields or a good purchase first. Consider upgrading by sector 3 or even 4. Other upgrades like sensors or the auto-pilot aren't worth it except to get some blue options on special encounters. If I get those it's only for fun and much later in the game after I got essential stuff.
Remember you can save power by turning off some systems you don't need! The medbay rarely needs to be on at all time and you can easily re-route power from the oxygen to engines to get a bit more dodge when the enemy fires. In fact you can have your engines unpowered until the enemy fires something, at which point you can pause the game, re-route power to fill the engines, see if you dodge and then unpower the engines. As long as the projectile hasn't reached your ship, it hasn't been decided if you are hit or dodged it. If they have ion weapons, you can also unpower the shields before it hits you so they won't be disabled; maybe another system will be hit but an ion shot on a shield layer means they will be disabled if you don't dodge and that can often mean you'll take a laser volley in your face right after. That kind of stuff takes practice but it can help a lot in the early game.
Don't bother to train your crew by having them dodge during weak enemy encounters. Yes, the little bonus you get to dodge or shield regen is always welcome but it can be tedious and you'll get it eventually. That said I sometimes do that when I know I want to run to the bathroom or make a sandwich and know for a fact I won't be hit instead of pausing the game.
This takes experience and practice or simply spoilers but know which events can result in a bad loss. For exemple never try the alien spiders event unless you got a blue option as it may result in the loss of a crew member and the rewards in case of success usually do not compare to the risk involved. Of course you do not need spoilers and it's fun to experiment but once you know, just make a note of not taking unecessary risks. You probably already know that one but it is worth repeating as I always decided to try every event which resulted in loss for me. Only after I decided to restrain myself did I actually manage to make some progress.
Little detail: never repair your hull to full. Try to keep it to 25 if you got scraps for repairs because some events may results in having some damage repaired for free. If you are already at full hull, that gift is lost and that's scrap you could have kept for upgrades.
The game is random, and that's in its nature, but I've learned that if you know how to maximise your chances and minimise your risks and making the correct call about the order of upgrades or purchases and knowing when to run and when to fight then you can often win against bad luck. And I'm still learning which is the mark of a good game.