Edit: I'll also go with the recommendations, the previous poster. Go with Beam Weapons and Torpedoes. However. I would reccomend 2 Beams and 1 Torpedo fore and aft. Trying to runn 5-6 beams and keep up your Auxiliary Systems power is going to bottom out your weapon power levels too much. I found that 4+2 much more effective in terms of overall DPS. And you shield use your maneuverability to take advantage of the Torpedo in the rear. And maneuvering also spread weapon fire over all of your shields.
In a Science Vessel you aren't in a DPS race. You aren't going to kill things quickly unless you get luck with your science BOFF abilities. The first thing is the head game. You aren't going to skill things quickly. You are going to kill them in (hopefully) complete safely. Because you are going to blind, hamper, kick below warp core, trip, confuse your opponents with Science! In other words, you fight dirty.
And science abilities are fairly strong, but they aren't going to defense your opponents by themselves. But using things in combination can weaken your opponents to the point where your reduced firepower + Sensor Analysis will take them out.
Let's take a oldie but a goodie Science Vessel combo. Come into weapon range with an Enemy Cruiser, hit them with Jam Sensors, then Tachyon Beam to weaken their shield (and which doesn't do damage to break the Jam Sensors sooner), Target Subsystem Shield which might drop the shields, Sensor Scan (If Science Captain), and then Torpedo: High Yield. Congradulations, you blew the plasma out of a Cruiser with it getting off a shot. Now even with the shields dropping, you've weaken the shields considerability, the lower power levels makes the shields have less damage resistance for the duration of the debuff. So the shields are much weaker and you haven't fire a shot yet.
And you can have different type of builds which can put opponent shields in very weak positions. You can have shield sucking builds with Tachyon Beam, Target Subsystem Shield I, Tractor Beam with the Tractor Beam DOFF which will drain shields, Anti-Proton Sweep ability from the Jem'Hadar Space Set and other ablity can weaken shield and make it easier for you to take out your opponent. And you can keep up the shield weakening in addition to weapon fire.
Or a power sucking build, Power Syphon, Energy Drain, and Tyken's Rift can drop ship power so that everything stop working. With Target Subsystem attacks, you can take out even a Borg Tactical Cube's for a short period of time.
Another favorite build of mine for multiple ship encounters, Scamble Sensors + Gravity Well followed up with Sensor Scan to help them blow up themsevles better and Fire At Will and Torpedo Spread.They shot at themselves at point blank ranges and you help them out with your AoEs.
And even individual abilities can be invauleable in certain situations. Tired of those True Way Galors being jack-rabbits with Evasive Manuvers? Well hit 'em with Target Subsystem Engine I of your Science Vessel ability. You'll stopped in their tracks or you'll slow them a lot even under Evasive Manuvers for the duration of the debuff.
Running a Science Vessel is probably the harderst character to get a handle on and to run well. Because you aren't a big beefy Cruiser which slugs it out wth Capital ships. Or a glass-cannon Escort. You need to get a build which you like to use and is effect for your playstyle. A well run Science Vessel in a team is a multiplier for the team.