Space battles are historically VERY popular things in science fiction. One of the most famous and popular sci-fi franchises in history is named Star Wars, after all. So with spaceships zipping around at Ungodly High Speeds, it might be a good idea to look at how they do damage.
Starships generally use one of three kinds of weapons: Projectiles, Guided Missiles, and Beams. All three are in use in the Aquarius Ascendant universe, in different roles.
Projectile Weapons are fast-firing, generally fairly easy on energy use, and hit pretty hard for their mass (Sir Isaac Newton is the deadliest son of a bitch in space!). The problem with projectile weapons is that given a reasonable energy budget and barrel length, you can only accelerate them to a small fraction of lightspeed, which both hinders their damage potential and gives the enemy an opportunity, probably a very good opportunity, to evade them at typical starship engagement ranges of several light-seconds.
Because of this, in the Aquarius Ascendant universe, projectile weapons are generally restricted to being used as last-ditch antimissile defenses (we’ll get to why later, but the short of it is, to do serious damage against a warship, a missile needs to score a skin hit). In a defensive condition, their lack of speed doesn’t really matter as much (because velocity is added to the velocity of the target projectile, and the enemy’s doing pretty much the opposite of trying to evade (because evasive maneuvers might throw it completely off of its firing solution and missiles generally only get one chance to hit).
Projectile small arms remain in general service, but that’s a subject for another post.
Guided Missiles are technically a type of projectile, but they’re a projectile that is both self-propelled and self-guided, so they fit into a separate category. Guided missiles are long-ranged, very fast, and hard to evade, but have one major issue: Because space is empty, the shockwaves that modern missiles use to generate a proximity hit can’t propagate (I use this in Independent Flight – a warning shot is fired several thousand kilometers in front of a target; the explosion is still ongoing as the target runs over the blast, but the fact that it hasn’t been hit dead-on means that it buffets rather than vaporizes the target). Furthermore, since space warships are heavily armored, the blast fragmentation effect used by modern air to air missiles to “saw” a target into pieces will have only minimal (or no) effect on a target with any real protection. Therefore, if a guided missile is going to generate a useful hit, it must generate a skin hit. As of the present day (343 SE in Independent Flight), point defenses have become very fast-firing in order to hit missiles, and missiles in turn have returned to the ancient technology of multiple independently-targeted attack vehicles in order to saturate point defense.
In terms of payload, guided missiles carry nuclear explosives for their primary warheads. Kinetic/momentum effects are significant, but the main blast is a thermonuclear explosive of hundreds of kilotons (for light warships), several megatons (for destroyers and light cruisers) or several tens of megatons (for heavy cruisers and battleships). They typically reach from three to twenty light-seconds in range, and reach speeds of roughly +0.2c with respect to their firing platform (with a commensurately smaller increase in speed closer to the speed of light due to relativity).
Beam Weapons: These are the main ship to ship weapons of the Aquarius Ascendant universe. Beams are very powerful and nearly impossible to evade. However, they take a great deal of power to fire, and beams attenuate over distance; the most powerful laser focused to the point of a pin will attenuate to the diameter of a dinner plate over a distance of roughly a light-second. Because of this, a laser hit at long range will do substantially less damage than at point-blank and be easier for navigational shields to shunt aside.
As implied in the previous paragraph, lasers are the most suitable beam weapon for space to space combat. Particle beams are attractive theoretically, but they are difficult to work with and have poor power intensity (the amount of energy transferred to the target by the particle beam for any given energy input is low). Plasma weapons are not a beam at all, and attenuate more or less instantly after firing.
The standard light to medium starship weapon is a gas-phase laser operating in the near ultraviolet. This is identical to the lasers we see in the modern world. A standard capital starship weapon is a “soft x-ray” laser (or “xaser”), which is of a type that we have yet to develop. This weapon uses a gravity-based reflector (modern mirrors poorly reflect x-rays). Grasers (gamma ray lasers) are seen as a hypothetical possibility, but the problem is that gamma rays interact weakly with solid matter, resulting in (once again) poor power intensity.
Lastly, visible-frequency lasers are used in the point-defense role, to shoot down missiles by overheating them to the point that they lose structural integrity and come apart.
Artemis Flight Books 
I actually wrote a series of articles about this a couple of years ago for Sci Fi Ideas website. I also did a couple on mecha that pissed off a reader bad. 🙂
One thing I forgot to mention:
There is no mirror known to current human science that will reflect a gamma ray, so a working combat graser would have poor beam coherence; prototype grasers have been referred to as “beam shotguns.” New technological advances may appear to change this, but the problem of gamma ray interactivity will probably persist.