I've said it before, and I'll say it again: it's the underdogs that always win. I just flew the Engi B to victory using both of the starting weapons and a halberd beam (only 3 weapon slots). I stuck a defense drone and a combat drone in the drone system, and I kept the anti-personnel drone for the whole game. I really struggled to get through the 4-shield enemies. It required a hit from the heavy ion, plus the combat drone in action, and a hit from the heavy laser, in order for the halberd beam to do some damage. I mean, it's taking the 'philosophy' of the Engi B to a whole new level.
The defense drone was priceless, probably saving me a ton in scrap repairs, not that I needed to pay, since I was given not one but two hull repair drones. The stats said this was one of my most scrap-profitable ships, at 2065 scrap (my highest record is only 2160).
And yet, although I struggled to get through four shields, I had some indispensable assistance from mind control (purchased around sector 4) and the cloak (purchased early). I didn't even need the cloak often, since the defense drone kept missiles away. I nearly defeated a ship using only top-level mind control.
I dunno how these hunks of junk make it through to victory, but I'm still picking the wrong winners. My success rate is about 10%.