ah yes, FTL, the awesome little thing that's about as frustrating as it is rewarding. Here are some general tips, based on by 100+ hours of gameplay:
Weapons:
1. Ion weapons are awesome, but you have to sync them patiently. In particular ion bombs are the bomb.
2. Bombs are alright generally, ion bomb being the best of the bunch, fire bomb second. Repair and healing bombs, situational I guess but I never use it
3. Fire based weapons are useful but not crucial
4. Laser weapons are really good, but use burst lasers over heavy lasers every time. Burst laser II is one of the most unbalanced and therefore best weapons you can find.
5. Beam weapons are good for early game, but towards the end, since they can't pen shields, have to be combined and synced with other weapons, probably bombs and/or ions.
6. Rocket weapons are probably useful, but I never ever use them for some reason, they waste ammo and are generally not as good as bombs.
Drones:
1. Attack drones are overall the most useful of the bunch, they can chip down shields and in sync with other weapons, can do pretty damage
2. Defense drones are selectively useful, defense II isn't worth the money tbh because it will fire at lasers and stuff which will likely be tanked by your shield bubbles anyway. Defense I is in my opinion better because it shoots down rockets and attack drones, which brings me to my next point
3. Boarding drones I never ever found all that useful, you can combine them well with a boarding party but it's often a waste of resources
4. Shipboard drones are quite optional, you can use them if you lack the manpower on the ship but far from necessary.
Modules:
1. Shields: aim to max them, but if not, 3 bubbles is a must
2. Engines: level 6 minimum
3. Weapons/Drones: Depends on how you play, that's customisable
4. Teleporter: Many people will say it's absolutely essential for the endgame, which is not exactly true, while you do make it easier, it's possible to win without it
5. Cloak: If available, sure go for it, but it's optional.
General tips:
You should use your first cash to upgrade your shields to 2 bubbles, what it does is protect you from most early game damage while providing your crew members to work on their skills. A proper layout can max out your crew in one fight, but it will take a bit longer though. After then work on getting your engine up and shields to at least 3, while balancing with your offensive tactics. Boarding is generally a more viable option than destroying, but you need to know your stuff.
Flagship:
If you can use the teleporter to pick away at individual modules, it's great, always go for rockets and ions first since those rooms are isolated and once killed, will stay dead for the entire fight. Then you have several options, you can either target the medbay to stop their healing and pick them off one at a time, but if you're not armed to the teeth, you might not be able to take down shields, kill the medbay and crew in between the flagship's cloaks. Obviously the best ships to use for this are Mantis and Crystal, Rock being distant third.
A defense drone would help a lot in phase 2, that's when the flagship sends a boarding drone to you, which, if it lands in cockpit, might cause trouble if you're not prepared and negate all of your evasion bonuses. The drones that will be sent to you in that burst more will be easier to defend then.
Third phase is a non-challenge if you made an effort to kill off the crew, if the crew is alive, it makes things more difficult and if you wasn't hurt bad in phase 2, you can manage easily. If none of the above was done, your best bet is to simply outslug them, coordinate your charge time and focus fire on its critical modules.
As for hard mode, I haven't tried it yet, but the flagship is done in a completely different way
