Part 1.
Without knowing a great deal about how the combat plays out (I watched the trailer, so it looks like an arcade style/FTL type system?), I might have some ideas.
I'll assume everything is relatively close range (like 1-15 KM, not the 10 million+ KM of the Honor Harrington Universe I dream about). It might also be worth knowing what speeds and acceleration you envision this happening in: some high acceleration rate (100+ gravities) would need some kind of handwavium 'inertial compensator' otherwise people would liquefy (which could be a critical ship system, blow it up and the crew dies, which would also allow the crew to move around like in the trailer).
Without knowing a scale, I'll just make an arbitrary one to illustrate my point; everything's out of ten.
Direct Fire: (Beams and ballistic systems)
Directed Energy Weapons:
-Coherent Radiation Emitters (lasers): Imagining an energy mount (not necessarily a turret), which could be tuned to emit different frequencies by increasing power output and wavelength. The emitter itself should have a power rating (which would act as a base determinant for damage and range), for example, a 100GW mount would have a greater base range and damage than a 10GW mount. Once you have the different mounts, you could add in ways to tune them, whether by having them in a static mode (only 1 frequency) or putting on an adaptive emitter which allows you to shift frequencies (the adaptive emitter would be very expensive, naturally). Once the emitter is selected, you could have each frequency modify the output of the mount; radio would be really long range, but have severely limited power, whereas Gamma Ray would be horrifically powerful, but very short ranged. In theory, a very large mount with a gamma ray tuning could out range a very small radio mount.
-Pulse Directed Energy variants; a twist on the above, but pulses the energy output allowing for vaporized material to vacate the area (when a laser strikes something, highly energized particles of that material form a cloud, which diffuses the beam, reducing focused output. Oscillating, IE, pulsing the output, allows that material to fly off, promoting beam cohesion). This comes at a cost of base range, as there has to be greater internal handling of the beam within the mount (more mirrors, switches to rapidly pulse the beam etc), but greater damage.
Different frequencies of CREs would cause ancillary effects; a radio laser would interfere with radar arrays, and could cook the crew akin the a microwave oven. An infrared laser would gradually heat the material of the target, and strain the cooling system. Visible light would dazzle optical sensors (kind of a boring spectra), same with UV. X ray and gamma would hammer everything, and cause damage to the crew (assuming the beam didn't outright kill them. Cancer!). However, there would be physical limitations on the CREs; the more powerful the weapon the quicker it is to burn out its components (higher maintenance costs).
-Charged particle weapons:
This article has a very interesting outlook on various weapon systems:
http://www.arclight.net/~pdb/hammer-lig ... index.html -CPWs are effectively lightening emitters. These would be very large weapons, since they need long runs to accelerate the particles to near lightspeed (C). Alot of sci fi weapons could be categorized as CPWs; Ion canons, proton beams, etc. The problem with CPWs in Sci fi, is that if people live in ships, the ships are assumed to be radiation shielded; thick lead walls, massive water tanks, etc. space is filled with charged particles thrown out by the sun, which as it happens are the same types of particles generated by CPWs. This isn't to say they are totally useless; a CPW could be used to batter a ships shields or dazzle/destroy sensors, missile tracking, drone command links, etc.
Kinetic Energy Weapons: Projectile weapons
There is really only two ways that a KEW could be produced; chemical propellants or magnetic acceleration. So, auto-cannons/artillery vs Railguns. In space, KEWs have an infinite range due to Newton's first law (glad someone mentioned the ME2 quote). The important things that need to be considered with KEWs is mass, acceleration, and velocity at the moment of impact. Whether it is a projectile fired by a canon or a railgun, once the bullet leaves the barrel, they both impact the same way. Where the differences start creeping in, is the ammunition and energy sources.
-AutoCannons, Artillery, etc. (ACs are fast firing small caliber, artillery is large caliber slow firing)
These systems would fire self contained chemically propelled rounds (all the energy required to fire the weapon is contained within the shell, thereby relying on potential energy). These systems would be virtually free to the ships power output; all the ship would have to power is the loading systems. The principle detriment, would be that the shells are massive compared to the rounds for a railgun. However, these systems could use some interesting types of ammo compared to a rail. Since the rounds are only subjected to massive G forces (not magnetics) they could have special payloads built in.
Since the projectiles are unguided (they might be rocket assisted, but putting guidance on them makes them missiles), they are relatively short ranged, due to their relatively low speed (space is huge), and the probability of a ship altering course.
-Plasma: As opposed to the Halo view of plasma as blobs of gas flying around space, a more realistic view of plasma weapons would be to siphon off plasmatic gas from a fusion plant into a containment vessel in the shell (which would require alot of high pressure ducting, akin to the view of T.C McCarthy's Subterrene series). These shells would wreak havoc on a ships shields, as the high energy gas would dissipate along the shield field surface (applying more energy over a greater surface area).
-Nuclear: An elegantly primitive thing, really. A small fission device stored in the payload. Would cause some explosive damage, but would have a reduced effectiveness since there is not atmospheric displacement. Would leave residual radioactive dust on the ships armor if it got past the shields, which would require maintenance.
-Fusion: An expensive micro fusion plant loaded into the payload. Would cause some damage.
-Antimatter: Very expensive, but also the most destructive. A small amount of Am would be loaded into a magnetic containment vessel in the payload. If it gets passed the shields, the AM would impact on the ships armor, resulting in a direct mass to energy reaction (mutual annihilation of the matter/antimatter), causing a massive amount of damage.
AC and artillery projectiles could also be rocket assisted, allowing them to have a higher impact velocity.
-Railguns: magnetically accelerated projectiles
Railguns focus on velocity on impact as opposed to the mass of the impactor. A 3 gram iron slug would hit much, much harder traveling at .99C than a 2,000kg projectile traveling at 30 KPS (fast for a chemically fired projectile). The charges for a railgun would also take up very little room compared to a chemical shell. Railguns would also be relatively accurate, their projectiles traveling at nearly the speed of light would reduce the ability for the target to move. The draw backs, however, are that a railgun requires massive amounts of power, and the inability to use special ammo (the magnetic rails would destroy any onboard electronics, such as containment units). Due to the nature of magnetism, it would also require the ammo to use a magnetic material, such as iron.
Missiles: ( as opposed to have a predefined list of missiles, develop your own)
Missiles have alot of potential. The easiest way to think of these things in design terms, is that they're little kamikaze ships. They have a propulsion system, a hull, command and control elements, and a payload. I would LOVE to see the ability to customize missiles. A missile could be built from the ground up by selecting different subsystems for each slot.
Payload: In theory any payload that could be put on a chemical KEW shell could be fitted to a missile, as well as pretty much anything else.
-Laser heads: To borrow an explicitly awesome idea from David Weber, a small fusion device is loaded into the payload compartment of the missile, along with a series of one use laser emitters. When the missile reaches attack range, the fusion plant detonates into the laser emitters, which focus and direct the force of the explosion into the target from a distance (he dubbed them 'bomb-pumped' lasers).
-Electronic Warfare platforms: Also from David Weber, these missiles carry a suite of electronic counter measures to confuse and debilitate a ships onboard missile defenses. They're there the assist the attack missiles reach their targets.
Guidance: simply put, the more research into missile guidance one has, the better and more effective the missile guidance would be.
-Resident AI: Instead of relying on the ships tactical section updating the missiles attack profile, a smart or semi-smart AI would use its own initiative to reach the target.
-Telemetry Guided: lightspeed telemetry links to the firing ship allows the tactical section to update their attack an ECM profiles, allowing them to try and get passed the targets missile defences. This would probably be a starting technological level.
Propulsion: As with guidance, more research = better propulsion. Improvable flight times, better maneuverability, better acceleration, etc.
Also, different missile sizes; E the difference between a cruise missile and an ICBM. You can fit more on a bigger missile, but it takes up more room (all of which should be improvable through research).