In space, everything is ballistic in nature.
It would be smooth, but not graceful. Both ships would be struggling to stay within their optimum ranges, and out maneuver the tracking speed of the enemy guns.
The whole thing devolves into firing mass drivers at each other from miles (and miles) away, then adjusting position, so that hopefully, the other projectile misses. Most of the time, the ships would be operating at such extreme ranges that the other ship would only be visible on instruments.
Imagine the scenario: Ship fires, several minutes pass. Gunner: "Negative hit sir" Sensors: "Incoming projectile" Captain: "Adjust heading to miss the projectile, re-target and return fire. Someone bring me a hot cup of Earl Grey."
If you have lasers, it's a game of "let's see how long it takes for you to have a hull breach", with both sides firing until either guns blow up, or the other ship does (from miles away, again):
Ship fires, several minutes pass. <PERSON>: "Their armour is holding, and they are returning fire." Captain: "Maintain fire, and deploy reflective plating. Keep an eye on temps" Ship maintains fire, several more minutes pass. <PERSON>: "Hullbreach reported by telescopics, and guns are starting to overheat". Captain: "Good, cycle lasers and heatsinks, and find us another target"
Small, maneuverable ships could be used, but not for dog-fighting; they would be used in boarding actions, and as they would see you coming for literally hundreds of miles away, the casualty rate would be horrific(think world war 1 level losses). If you could invent some form of stealth tech, this could make for exciting boarding marine action.
The only way to have dogfights be viable, is for the ships to have reactionless, low inertia drives, which enables fast changes in velocity, with little in the way of G-forces. 898
At this point, the motion of the ships would be erratic, making long range artillery utterly pointless outside bombarding space stations. At this point, the motion of ships would be jerky and erratic, as they try to do the same thing all pilots have since aerial warfare began: getting behind the enemy(where there are typically no guns), and shooting them. This is your basic star wars/battlestar galactica, star trek etc fare.
So, for your world, You have to decide what space combat will be like:
1. Dogfighting, using "magic" propulsion which also gets rid of G-forces powerful enough to liquefy a man.
2. Long range artillery duels, using missiles, point defence guns, armour and mass drivers.
3. Ships with heavy armour on the front. These ships simply ram into the other ships, to cause as much damage as possible. Basically steerable missiles with a crew.
4. Laser combat. More long range engagements, with each combatant trying to melt through the other ship before the same happens to them.
Basically, unless you use some space magic, space combat is going to be dull, and uneventful, until something actually hits, then everyone dies, as the ship now has a massive hole in it. 898