Maneouvrability is a potentially significant advantage in almost any battle. But, the maneouvrability of a spacecraft with inhabitants is limited by the inhabitants's tolerance to accelerational forces. Humans generally can't tolerate high g-forces for a long time. Even to horizontal g-forces, which are more tolerable than vertical g-forces, untrained humans can tolerate 20 g for less than 10 seconds, to 10 g for 1 minute, and 6 g for 10 minutes (Source : Wikipedia). The limits for trained humans may be higher, but not much higher.
Considering that, I put forth a system, where most battleships are remotely controlled from specialised control ships, where the crew are. A crew member sits in front of a computer, controlling what he is in charge of. He sees what he needs to see, and not too much else (e.g. a gunner sees his field of fire, whereas the admiral sees the entire battlefield).
Obviously, in such a system, the most valuable targets would be the control ships, much like the generals were in historical battles. The loss of a control ship means that all the ships controlled from it lose some degree of control (not necessarily all control, since the other control ships can take it over; but they only have basic control such as "move there", "fire the forward guns", "self-destruct", etc.). The loss of all control ships means that the battle is lost. Because of that, control ships are generally the most well-shielded.
Details on FTL travel:
Ships can travel to the battle site faster than light but can only battle at subluminal speeds.
Faster-than-light travel is done through "hyperspace" and has a 15 minute recharge time, ship time (after emerging from hyperspace, ships need 15 minutes before being able to activate FTL again)
FTL travel speeds vary from 10,000 to 40,000 times the speed of light, with the average being 20,000 c.
A ship retains its direction of movement when entering hyperspace, and upon leaving hyperspace its speed reverts to the speed before the FTL travel. For example, if a ship travels at 0.001 c and enters the hyperspace, upon leaving it its speed would be 0.001 c. Corollary : If a battleship were to travel FTL in a direction it's not heading towards, it either uses the subluminal propulsion system to adjust its direction then actiivate FTL, or activate FTL first, emerge in a relatively safe location, adjust its direction while waiting the 15 minutes, and activate FTL.
A control ship can travel FTL, but if it's not travelling FTL, its acceleration is limited by the crew's tolerance.
FTL communication without FTL travel is available, but the transmission and reception facilities needed is too large to be put in a ship. Such faclities are generally built on planets. Therefore, ships in a battlefield communicate at no more than c.
Details on combat capabilities:
Ships only battle (fire guns, launch fighters, etc.) at subluminal speeds. Guns can be fired in hyperspace, but why waste ammunition?
Battles are conducted at a range of about 1,000 km ("close quarters") to 300,000 km ("long range").
Battleships and control ships have shields; shields deplete as energy (including kinetic energy but not including the $E=mc^2$ mass-energy) is thrown to it.
Shields stop only incoming projectiles etc.; shots from inside are practically unaffected.
A ship generally can take 20,000 hits from "standard-issue" guns (which are the most numerous of the guns), a large battleship can take 30,000, a control ship can take 40,000. Missiles are about 10 times more effective, but 20 times fewer. Battleship main armaments can take down a control ship with only 40 hits. A control ship can usually be destroyed with a 200 MT of TNT weapon.
Most of the weapons used are subluminal; projectiles travel at around 20,000 m/s.
How far from the other ships would the control ships be located? What distance is a good compromise between response time and safety?
The ships travel as fast as needed (and tolerable, for control ships). Remember, this is space, there's no atmosphere to slow you down. So acceleration is more important. Control ships are usually capped at 1 g, but can accelerate to 6 g for a short time. Other ships can reach 100 g on average, with the range being 40 g (heavy battleships) to 250 g (fast, small ships). Fighters can reach 400 g.
Control ships are about 750 m long, heavy battleships 1,500 m to 2,000 m, fast cruisers 500 m.
Let's say communications technology has developed to the point the equipment is resistant to being disabled, and that communications can't be intercepted nor faked (one side can't control an enemy ship).
You can't just disguise a control ship as a controlled ship; sensors are available which can detect shield strength.
A shield extends to hyperspace forming an "umbrella". Trying to emerge on or near a shielded ship results in prompt, utter destruction of the attacking ship, and little damage to the attacked ship almost regardless of the previous speed of the attacker. (But yes, if the ship's shield is down, an FTL attack can take down the ship.) The umbrella is about 15-20 km in diameter.
If a fighter starts from zero speed and uses all its fuel to accelerate in a straight line, it can reach 5 MT of TNT equivalent.
Fighters can't travel FTL. The smallest ships which can are about 300 m in length.
Each crew computer has a toggle for "automatic mode", in which it takes general orders (such as "fire at that ship every 10 seconds") and executes them automatically. But, the operator can override it or disable it altogether.