After a couple of iterations, I pieced together a Eng Cap/Sci Ship build that I really like. Good for PvP + PvE. Pardon for not having all of the levels on-hand, but the descriptions should give you an idea of what it can do and how to play it.
Very little systems overlap, so global cooldowns are basically a non-issue. The build is basically a Sci-based dogfighter.
Recon Science
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Offense - Sci
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Tychons Rift III
Tractor Beam
Feedback Pulse
Charged Particle Burst
Photonic Shockwave
Offense - Tac
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Torp - High Yield
Torp - Spread
Fire at Will
Healing
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Eng Team
Hazard Emitters
Emergency to Shields II
Rotate Shield Freq (captain)
Gear
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5 Polaron Beam Arrays set to autofire
1 forward facing RapidFire Transphasic torpedo (breen)
Tac : 3 polaron consoles
Sci : 3 particle emitters
Sci : 1 shield (+35%)
Eng : 1 turn rate boost
Eng : either Ablative Armor (PvP) or Assimilated Console (PvE) (not firm yet, still experimenting with ablative)
3 pieces of Aegis for Reactive Shielding (it's amazing!)
Note that my captain maxed out Hull integrity and bought a few ticks of Energy Resistance for the Hull. I can hull tank for a fair bit, especially if the Reactive Shielding gets a chance to boot up... the main reason for Ablative and the shield boost. I'm generally of the philosophy of covering your weaknesses, and hull integrity is the main one for the ship.
On approach, unleash a torpedo spread while in Aux mode, drop a Tychen and tractor (keeps them near for draining), hit feedback, then switch to Weapons mode.
Tyken + transphasic + Feedback Pulse allow direct hull hurts even if someone has a ton of shield regen.
Polaron + Tyken and/or shield targetting allows the occasional bare hull abuse.
It's fun.
