Ok, I have Nebula (Adv. Research Science Vessel) now so what kind of setup I should be looking for? I' prefer to have healing when I am in fleet action and offensive (of course) when I am going solo to cleanup the sectors to earn Accolades

Currently I have:
Phaser Dual Beam Banks x 2 (Front) Mk VI
Quantum Torpedo x1 (Front) Mk VI
Phaser Beam x1 (Rear) Mk VI
Quantum Torpedo x 1 (Rear) Mk VI

Science Lt. Commander: Gravity Well I, Energy Siphon I, Polarize Hull I
Engineering Lt: Engineering Team I, Reverse Shield Polarity I
Tactical Lt: Beam Overload I, Torpedo: High Yield II
Ensingn Universal (Science): Transfer Shield Strength I

Consoles:
I don't remember what consoles I have as I am at work now but I'll post those later

Anything I should change to get the desired level?

Oh you are flying the Tier 4 Nebula; not the Refit.

Drop Energy Siphon and pick something else up. I recommend Tachyon Beam 2 or Charged Particle Burst 1.

Drop Reverse Shield Polarity and pick up Engineering Team 2 or Auxiliary to Structural 1. Drop Engineering Team 1 and pick up Emergency Power (Weapons) 1.

Switch Tactical powers; High Yield Torpedo 2 isn't much more effective than High Yield Torpedo 1, while Beam Overload 2 is much better than 1.

I've only been using the refit Nebula, but you might consider using standard beam arrays instead of the duals. It might just be how I fly, but the larger targeting arc does a lot for me.

Maybe someone else can say about whether it works in pvp, but energy-level powers don't have a ton of effect against ai ships. I'd second what KillingMeSoftly said about the tachyon beam. Combining that with beam overload and then dropping a high yield once your enemy's shields are down can do a lot of damage quickly.