For a primer on space combat and weaponry go read Atomic Rocket's: Space War and the follow-up materials on the weaponry. In fact, you should do that before you read any more of my answer.
A quick summary of the science is:
- Fighters are unrealistic
- Stealth is unrealistic
- Shields are unrealistic
- Armor is not practical
- Weapons all come from 2 basic forms (directed energy or projectile) with lots of variety.
I am going to challenge you on your constraints (e.g. no lasers). I think there could be a way to get what you want and keep those in.
There will be two main categories of weapons, directed energy weapons (this includes lasers) and projectile (this includes guns, missiles, and anything else that is not a directed energy weapon).
Most of what I have to say about lasers applies equally well to other types of directed energy weapons (e.g. particle beams of various types).
Forget everything you've seen in SciFi about space lasers. The most effective laser is one that has lots of power and a large primary mirror to focus the beam at a distance. So a Traveler RPG type "spinal mounted" laser with two pop-up turrets (one on each side of the ship) might be the way this is accomplished. This gives you 1 lasing cavity with two apertures. One can be doing target tracking while the other handles the shooting.
The "spinal mount" might be a Free Electron Laser (FEL) so that you can tune the laser to any wavelength (e.g. for beam reasons, this will probably be X-Ray). You might get an effective kill shot on a ship of the same size all the way out to 1 light-minute distance (11 million miles or 18 million km).
The beam travels at the speed of light (or for particle beams, close enough that you'd have a tough time telling the difference). The targeting is only as good as the physics allows. Meaning at 1 light minute distance, your target has 2 minutes to get out of the way of your incoming fire.
Projectiles actually covers a couple of different groupings. Weapons with propulsion and guidance and those without. You might call weapons with low thrust but high $\Delta V$ torpedoes and weapons with high thrust but low $\Delta V$ missiles. Both would require guidance.
To ensure a near miss would still kill the target, most of these will include a nuclear warhead. Note a 1 km miss with a nuclear warhead means no damage to the target. You might even miss by 100 m and not inflict significant damage (depending upon warhead size).
An alternative to projectiles with propulsion and guidance would be completely dumb projectiles. All of these (chemical powered ones, gauss/coil guns, rail guns, gas guns, etc.) might be classified as "guns". The problem with these is that they're really only good for close range. Against a maneuvering foe at a 1 light-minute range you have almost no ability to hit a target with them - no matter how good your computer targeting is.
An alternative to fighters
The Atomic Rocket's site states that fighters don't make sense. The pilot actually significantly reduces the survivability of the platform. However, the concept of fighters still makes sense: project weapons into locations too dangerous for your big space cruiser.
So they use the idea of a Kinetic Kill Vehicle Bus. It's a "missile bus" that drives the passenger missiles into an engagement envelope so that the missile's on board propulsion and guidance can complete the intercept of the enemy ship.
- It's possible the KKV bus uses a low thrust high $\Delta V$ engine
while the missiles provide a high thrust, low $\Delta V$ engine for
the terminal maneuvers.
- It's possible the KKV bus provides extra computing power and penetration
aids to distract your target's defensive systems.
- It's possible the KKV bus provides telemetry and recon information back
to the mother ship. Which makes it valuable in the battle even after it
flies past the target ship.
- It's possible that the KKV bus may also attempt a target intercept if the
target is in the KKV bus engagement envelope.
Regardless of what you put on it, the KKV bus is on a one-way journey. The energy costs of getting it to return would be too high. If you read the Honor Harrington books, this would be very similar to the "Apollo" which they launch with their missile salvos as a control node.
A KKV bus has several advantages over "space fighters" and shares all the advantages of a manned "space fighters". The first is that they can maneuver at significantly higher accelerations than any manned craft - possibly up to the 10,000 g accelerations. They don't need to carry any of the life support equipment to keep a human alive. Best of all, they don't need any equipment for recovery, each is expendable with all that means for performance, size, cost, etc.
Using a KKV bus to deliver a MITW (multiple independently targeted weapons) instead of just launching those weapons en mass has some advantages. The first is that the vehicle can carry extra equipment to improve the performance of those missiles (sensors, penetration aids, communications, etc.). The second is that for engagements with unfavorable kinematics, the KKV bus can use different (high impulse) propulsion to provide the necessary total $\Delta V$ required for an intercept.
This does not make a KKV bus a requirement for such high $\Delta V$ missions - a clever war fighter might provide his side with multi-stage missiles in which the first stage had similar high $\Delta V$ capabilities. However, the KKV bus provides a bit more flexibility than simply extending the range of the missiles.
In space combat there are certain advantages that go along with different engagement aspect ratios.
A very non-exhaustive list:
- A tail chase favors the attacker because the attacker can always
turn inside the defenders turn radius.
- A tail chase favors the defender because projectile engagements
require less $\Delta V$ to hit the enemy (you can leave mines in
your opponents path).
- Head on engagements favor directed energy weapons over projectile
(it's difficult for projectile weapons to successfully intercept).
Directed Energy vs. Projectile
The laser ship (directed energy) will try to get close enough to the projectile ship so that their laser can get a kill and so that the targeting light-speed delay is short enough that the laser can hit the other ship before it moves. While the enemy fires missiles, the beam will be tasked with shooting any missile which looks like it is within an effective engagement envelope. Priority will be given to hitting the KKV bus before it launches its payload of missiles. One turret will be acquiring a new target while the other turret is firing. As soon as the current target is destroyed, the beam will switch turrets and the roles will reverse.
The projectile ship (kinetic energy) will try to stay outside of the laser ship's effective range. They'll fire a barrage of KKV buses at the laser ship. They will try to saturate the laser ship's defenses. A laser ship will be able to fire more shots than a projectile ship so the projectile ship needs to complete the defense saturation as quickly as possible. After an engagement the projectile ship will need to restock its inventories.
Weapons Visible to Human Crew
Rather than making the weapons visible (especially at the range of 11 million miles!), what the human crew might be seeing is their defensive computers projection of the enemy's aim point.
Alternatively, if the enemy ship is directly firing projectiles or missiles are approaching you, then your defensive systems will definitely be tracking those objects and providing the human crew with probable trajectories. For projectiles with propulsion, the result will be a 3-dimensional shape representing the incoming ordinances propulsive capabilities (this is sometimes called a basket but it is usually not basket shaped). CJ Cherryh provides an excellent treatment of craft and weapon probable locations based upon latest data, known hardware capabilities, and light speed delays
If the enemy is firing directed energy weapons, you obviously won't see much of the beam unless it hits you, but it is possible that if your sensors are good enough, they could detect the passage of a powerful laser weapon based upon reflections from dust and gas. The computer could provide that feedback to the crew too.
The crew would have up to minutes to respond to the threats.
Basically, instead of making the weapons visible to a human's naked eye, the combat information system is overlaying all of its information on the map/screen and providing the human crew with information about probable trajectories, laser misses, aim points, etc.
If your enemy is pointing a multi-gigawatt FEL laser at you and their probable aim point is at the bridge, it would give the crew of the ship, the same feeling as if they saw incoming tracer rounds from that same ship.