Well, my character is an Engineer, and I fly an Odyssey-Ops instead of a Galaxy-R, but I'll give you the setup I am currently running, which might help give you ideas.
This ship is designed specifically for Cure Space, and is what I call a 'Defense Cruiser'. It is designed primarily to defend a single unit against oncoming NPC ships, and so it has primarily the goals of stopping enemy forces on a known intercept course as quickly as possible and providing support to the unit being defended:
Modified for the Galaxy-R:
Fore Weapons: 4 x Dual Beam Array (I use Mk XI phasers at the moment, but choose your own damage type)
Aft Weapons: 2 x Beam Array (same damage type as the forward weapons), 1 x Quantumn Torpedo Launcher, 1 x Quantumn Mine Launcher
Tactical Consoles: 2 x Damage Booster for the selected damage type of the forward weapons
Engineering Consoles: 4 x Ablative Hull modules (high resistance vrs. Plasma and Disruptor damage)
Science Consoles: 1 x Saucer Seperation Module, 1x Assimilated Module, 1x Field Module (shield point booster).
Engine: Borg Impulse Engine
Deflector: Omega Deflector
Shield: Omega Shield
Lt. Tactical: Tactical Team I, Beam-Fire At Will II
Comm. Engineering: Emer Power to Weap I, Rev Shield Polarity I, Emer Power to Shield III, Extend Shields III
Lt. Comm. Engineering: Emer Power to Shields I, Aux Power to Struct Integ I, Extend Shields II
Ens. Engineering: Engineering Team I
Lt. Science: Hazard Emitters I, Transfer Shield Strength II
Sorry for the generalizations and any wrong names for the modules (I am at work and don't have the info right in front of me), but it should get the general idea across. The tactics for this ship revolve in having two copies of Extend Shields to constantly have one on the ship to be defended, and to lay down mines while firing the four dual phaser arrays at incoming enemy units. I usually get into the flight path of the oncoming units and then move in reverse, firing as I withdraw towards the unit I am defending.
In other STFs, this ship would be protecting other ships of your team and moving to target individual targets of importance. The most important thing to remember is that this is a flagship/support unit, and is primarily concerned with protecting other ships rather than attacking the enemy.
Since you are a Science commander, you will have to adapt the above to your skillset, but I thought providing an example of my own setup might help you with ideas for your own.