Ship Weapons
Generally, Turrets use twice as much Energy, but do twice as much damage, either doubling shots (Gaining Double Shot or Double Shot -> Full-Auto), or doubling the damage dealt by each shot.
While I haven't tested all the weapons, I find Missile Turrets to be highly effective, since they have a low energy cost and do Kinetic and Burning (meaning they are good against Shields, which have a resistance to Kinetic, and Armor). They also have +10 Accuracy, which benefits whatever other weapons you have.
You could also have 1 weapon for Shields (EM or Laser), and another for Armor (Machine Gun).
You could also get your Systems up (80 is enough to likely succeed vs Dr Teyaal's MS-XI) and use a Shield Vampire to strip the target of their Shields.