A lot of this can be found on the Atomic Rockets website (http://www.projectrho.com/public_html/rocket/index.php), the Unwanted Blog (http://up-ship.com/blog/) and Rocketpunk Manifesto (http://www.rocketpunk-manifesto.com), but there are a few details which can be summarized here:
The range of weaponry in space and how they affect targets is quite counter intuitive to how things happen on Earth. Rifle bullets, railgun slugs and other kinetic weapons actually have effectively unlimited range, because in the vacuum of space, they will continue going until they hit something, If you miss your target, that "something" might be a rock in the Crab Nebula that is hit 11,000,000 years from now....
Similarly, rockets, missiles and torpedoes (any sort of self propelled weapon) are going to retain kinetic energy even after burnout. The main issue here is that so long as the weapon has fuel and reaction mass, it can still attempt to achieve an intersecting orbit with the target, so "range" is a function of how much fuel and reaction mass it has, and how much deltaV can be applied to reach an intersecting orbit.
Nuclear weapons are strangely ineffective since there is no atmosphere to create blast effects or convert x-ray radiation into other forms of energy, so nuclear warheads need to become the "drivers" for other forms of weaponry like x-ray laser bundles or nuclear shaped charges.
Particle beam weapons are affected by both "blooming" as the mutual repulsion of particles force them apart and the beam spreads, and also can her affected by magnetic fields. A particle beam duel fought around the orbit of Jupiter will see beams snaking and weaving in the Jovian magnetosphere, rather than arrowing into the target.
Finally, laser weapons can become death rays of stupendous range. In the Atomic Rockets site, there is a worked example of an x-ray laser which can carve through steel, carbon finer and ceramic at a range of a light second (slightly less than the distance between the Earth and the Moon), and is still incredibly dangerous at a distance of a light minute. The effect of the beam are notable to unshielded targets a light hour away.
Now while it is theoretically possible to launch railgun slugs from the Moon at targets orbiting Pluto, this is actually nonsensical for any sort of "hard" SF setting. Realistic combat operations would need to have enough time to track the target, predict its future course in the time frame for the weapons effects to arrive and be able to see the strike and make corrections.
From a practical viewpoint, space battles will probably be fought from distances ranging from practically point blank (in low orbits, where targets can pass at high relative speeds and disappear behind the horizon or drop into the atmosphere on a planet like Earth or Mars), to one light second, where the Ravening Beam of Death lasers (RBoDs) can quickly track and strike targets without targets being able to dodge the beam. The distance inside a light second is also easily crossable by kinetic energy weapons like railguns or missile busses in a "reasonable" amount of time. New Horizons made it from the Earth to the Moon in about 9 hours, which gives you the idea of the amount of "lead" you might have to program into a firing solution. It also tells us that a realistic missile weapon would be about the size of an ICBM (and New Horizon was actually launched on an Atlas, which was designed as an ICBM long ago). Railgun and coilgun weapons will also need to be very large and powerful to achieve similar or greater speeds, so a "gun battery" on a space warship would resemble the gun turret of a battleship more than a 20mm Gatling gun.
So for space battles, think of spacecraft the size of nuclear submarines or aircraft carriers, mounting massive weapons emplacements or laser generators. These ships will be in mutually supporting "constellations" capable of seeing and shooting effectively at targets out to a range of one light second, although capable of doing damage much farther away.