- Try to keep a minimum of 40 or 50 scrap at all times. If there's something super rare and awesome in a store then get it; but there's a lot of encounters that'll get you repairs, equipment or crew members at a reduced price and it sucks when you can't afford them.
- Level 2 shields ASAP. Many ships simply won't be able to break through, which means you go from taking as much as 4 or 5 hull damage per fight to 0. On easy (which I recommend playing until you really get a feel for the game) you really shouldn't need to upgrade past that until the last two or three sectors. I also recommend upgrading blast doors early on as it's really cheap and buys your crew members time to heal if they need to retreat from intruders.
- Unless you're so low that you're worried you might die in a fight, don't bother repairing hull damage at stores. There's tons of encounters that give you free or discounted repairs. Also, if you happen to find a hull repair drone then it's cheaper to buy drone parts and use hull repair drones than to actually pay store price for repairs. Don't buy the drone at the store though, it's not worth it.
- Try using Engi A, as its starting ion weapon has a ridiculously good fire rate. If you aim it at their shields, they won't have any...but I personally prefer to aim it at their weapons so they can't shoot back and I can just take them down at my leisure. Once all their weapons are disabled, switch targets every shot between weapons and something else - it shoots fast enough to keep them both ionized. I usually switch between weapons and shields just to make battles quicker, but sometimes they'll have another system that's a pain like drones or a teleporter. IMO if you're using Engi A and taking any hull damage at all in the first few sectors, you're doing it wrong (or you just got unlucky with misses

- Don't use autofire with missiles, it's wasteful and not really necessary. I usually just toss one at their shield room so that my other weapons can start doing damage, then leave it at that. Honestly, I've never really found missiles too useful except for hull breach.
- Fire weapons are awesome...fire not only disables systems, but forces crew members away from their stations to put it out (and hurts them while they do it). Fire drones are especially awesome because they have a high fire rate...they'll burn the ship up faster than the crew can put the fires out.
- Killing the crew while leaving the ship intact gives you greater rewards. Fire weapons are great for this, or you can just ionize the O2 system until they die (or both!).
- Mind Control is god tier. Just MC their pilot and they lose all evasion...on top of that, he'll start attacking systems like a boarding party and other crew members will leave their stations to fight him.
- Take your time with beam weapons and aim them well...against most ships, if you're hitting less than 4 rooms per shot there's probably a better way you could aim it.
- Dedicate one or two crew members to all repair tasks, so that they level more quickly and can repair faster. You can always dump more crew into a room in an emergency.
- I've never once upgraded my medbay and don't really see the point. Same goes for O2.
- If you have the opportunity to pick up a Zoltan crew member, DO IT! That's less scrap you have to spend on reactor upgrades.
- Timing of shots can be very important. For instance, the Engi A strategy I outlined earlier requires proper timing to work well. Target their weapons with your ion blast, then launch your combat drone about a half-second before the ion blast fires. The drone will hit their shields, dropping them so your ion blast can hit their weapons. Now here's the beauty of it: your ion blast and the drone have slightly different fire rates, so this cycle of "drop shield, hit weapons with ion" will continue for a few shots but then your ion blast will start arriving when the shield is up, which ionizes the shields and lets your drone do damage.
That's all I can think of for now, hope it helps. More experienced players, call me out if I'm wrong on anything

*EDIT* Just got reminded of this one (Fuck you, FTL): Avoid nebula sectors unless you REALLY need to slow the fleet down or there's no other path. Ion storms will ruin your day.