Contrary to some fanboys, a successful game of FTL seems to me to be more-or-less equal parts luck and skill. Often, a ship build idea must adapt and change and sometimes ultimately fail as the game progresses because loot is random and stores have so few items (I'd love for stores to have greater selection in a future edition or expansion). When a build does come together well, however, it's a fantastic experience. What are your favorite ship builds? Here's one of mine:

*** KESTREL CRUISER TYPE-A ***

WEAPONS:
(selections have great power/damage ratios, & weapons system can suffer some damage without losing offensive potency)

2 x Burst Laser Mark II (2 power, 3 shots, 1 damage per shot)
- one comes equipped; can substitute Burst Laser Mark I for other; easier to find but uses same power for 1 less shot/damage

1 X Artemis Missile (1 power, 2 damage)
- comes equipped

1 X Breach Bomb Mark II (2 power, 3 personnel damage, 3 system damage)
- can substitute Small Bomb; easier to find & saves 1 power at expense of 1 damage

DRONES:

2 x Defense Mark I (2 power)
- NOT Defense Mark II; primary concern is shooting down incoming missiles
- deploy only as many as needed per combat based on enemy weapons

AUGMENTS:

Automated Re-loader
- combined with a two-star weapons operator, produces a terrifying rate of fire

Long-Ranged Scanners
- too useful to pass

Drone Recovery Arm OR Adv. FTL Navigation
- tough choice; Drone Recovery Arm probably more useful, but Adv. FTL Navigation nice for The Last Stand

SYSTEMS:

Shields (Level 4)
- Superweapons? What superweapons?

Cloaking (Level 1 or above)
- Alpha strike!

Doors (Level 3)
- improved blast doors very useful against boarding drones/enemy crew

Teleporter (Level 1 or above)
- collect more scrap by eliminating enemy crew without destroying their ship; useful against boss

Other: Upgrade all systems to max possible with collected scrap to be able to sustain more damage without requiring immediate repairs.

This ship *toyed* with the Rebel Flagship: blasting its systems, eradicating its crew, setting it on fire, watching it burn, delighting in its slow destruction until the final command "Fire all weapons" was given when the boss had one hull bar left. Twas a good game. ;)

Ion weapons. [Burst II, preferably]. Then add some of the more fun beam weapons - if you can get two of the same type firing at the same time, especially. Slice them up (or burn them out). Can't dodge. Hit even if they engage cloak partway through.

Drones & Drone Recovery are a must; defense drone II is useless; beam drones better than anti-ship ones. Likewise bombs (breach II / ion bomb) rather than missiles.

Or just teleport everything dead.

The best ship is the ship that still has hull points left. :)

I think the builds that are most fun to play are not necessarily the killer ones but the ships that you really struggled to get through with (because of luck and/or mistakes...) so you'll have to play smart to finally be able to beat the boss.

My last run i barely managed to hold my Kestral B together through 6 and 7. Hull down on 4-5 and I didn't manage my resources very well so got stranded a few times. Living on a bare minimum of scrap and fuel and whatever stray weapons I could get my hand on I picked up the teleporter (had two idle Mantis...) and the 2/room beam (Halberd?). Not an optimal combo but with careful play I scraped enough scrap to upgrade shields and engines to maximum (after a few encounters in sector 8 where I ate the crew...).

I did have a drone control but never got the opportunity to get the Defense I...
The maxed out engines worked rather well as a poor man's cloaking.
Going into the final fight my weapons set up were surprisingly strong with Burst II, Heavy I and good ol' Basic Laser as support for my monster beam. (Although the encounter with a level 5 shield automated scout with missiles and bombs was a bit too much and a quick escape was needed...)
As for augmentations I think I had the Reloader (nice with any beam!) and Advanced FTL (I have literally never found a use for this...).
(It's a shame you cannot see the end build for your ships in the high score list...)

In the first boss fight my boarding party is sadly lost. They manage to take out the missiles (crucial since I have no cloaking or defense drones) and the crew member for the heavy lasers. My last volley does too much damage (I didn't count on the flag ship jumping before going to 0...).

Taking out the crew was however all that was needed since that means they won't be able to repair weapons in the next stages.
With the maxed out enginges (>50% evade) and shields I managed to avoid getting too much damage from the drones in stage two. No cloaking necessary :)
The last stage was basically a walk in the park. My attack drone took well care of the Zoltan shields, their boarding teams suffocated to death by means of my level 3 doors. They had only one crew member left on ship, occupied with the fire in the shield room. Halberd beam is evil (Heavy Laser didn't help them either). Missiles could have helped them but since my mantis boarding party (RIP) ate their missiles officer they had no way of keeping them live for more than two or three volleys.

And these are really the builds I like playing, even though it feels hopeless at times, where you go into the last fight not knowing whether you're strong enough and still manage to rip them a new one :)
I've not yet managed to get the shop boycott achievement. Maybe next time :)

Otherwise I feel like the builds become pretty similar, regardless which ship you went in with.
Enough lasers to break through their shields + a little extra :) Worst case, missile or bomb to damage shields.
Shields level 4 (3 may be ok as well)
Engines level 5 (gives > 100% evade when cloaked)
Cloaking (level 1 is enough)
Boarding level 1 or 2 to keep the scrap amount up.
Doors level 2, 3 if you're low on crew (or like watching them suffocate).
Defense drone MKI, possibly an attack drone if you have problems with their shields.
As for augmentations the scrap collector is really unmatched in strength, although the pre-igniter is madly powerful if you're sporting a burst III and a slow beam.

It'll be nice to explore the new possibilities in Advanced Edition!

I was SO close to beating Normal with the Kestrel five minutes ago. My setup was pretty much just this:
- 2 x Burst Laser Mk II and 1 Ion Bomb
- Max Cloaking
- Three shields
- Hacking 1st tier
- 35% evasion from piloting + engines
- Four crew members

My only downfalls were:
- before the third phase, I thought I'd jump somewhere else and come back to base so that they would heal me a little: well they didn't
- I only got more damage during that jump...such a stupid move all in all
- Once I had like four hull left and the enemy had about five, I Ion Bombed their shield and fired the bursts: I think only one hit, if even that even though the coast was clear
- The cloak was still reloading, and then the enemy used that one mega attack which finished me off.

Gah, it was so close! All their crew had died, all their regular weapons were destroyed...if only those last two laser bursts would had hit. I'm definitely gonna try the same setup tomorrow: that is, if I'm lucky enough to find one burst laser and the ion bomb. I really liked this ship build: doesn't take a whole lot of resources to set up.