Basically, just what the title says. What would be the range that most spaceships fought at if both ships did not have faster-than-light technology, but had railguns, slug throwers, and missiles? 100 km? 1000? 100000?
Also only speed of light sensor and communications
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.
It depends upon how good your missiles are, and how fast your slug throwers can aim (amongst a lot of other things!).
Either you'll have incredibly close quarters battles (in relative terms) as your missiles don't have enough fuel to engage reliably at a distance and your opponent can just move out of the way of unguided projectiles, or you'll have incredibly high tech battles that are fought from across solar systems and are basically decided by who can throw enough missiles to overwhelm the opponent's point defence systems.
In the first scenario you have two options for methods of engagement: one is the Lost Fleet style 'two fleets tearing past each other at a reasonable fraction of C and letting their automated systems throw metal slugs at the opponent', or you can go down the Warhammer 40K route and have heavily armoured behemoths that slowly match orbital velocities while hammering away at each other. In either scenario you're talking engagement ranges measured in kilometres, which is a terrifyingly small distance in space. These battles will be short, brutal, and have enormously high casualty rates.
In the second scenario you have the options of the Battlestar galactica style 'I throw missiles at you, you throw up flak screens to stop them', or you can have the Andromeda style 'automated drones fight each other at a distance, whoever has the best drones wins'. In either case as long as your missiles have relatively low fuel requirements and relatively high impulse thrust your engagement ranges can stretch up to infinite, limited only by the speed of light and how automated their control systems are. I'd reckon distances measured in light minutes, though it's really up to you. In either case if defensive technology (slug throwers) are more effective and cheaper than the offensive (drones and missiles), you'll end up with slow but grinding battles of attrition.
There are a whole host of other factors that can influence this, including communication tech, sensor technology, armour and shielding, and even the economic state of your opposing sides (weaker economies will favour better defences), so I'm not going to go much further, but hopefully this will help you work out how you want to define your engagements!
