Projectile weaponry would be fairly worthless given laser based counter measures that can shot down your projectiles long before they will reach their target. The only way to get them to hit is to overwhelm the defense system, which means huge amounts of resources wasted in trying to hit a target.
So the vast majority of weapon systems will be energy based. Lasers will not be visible until it hits you since it's moving at the speed of light. So in that respect you probably would not even see it until it's hit you. In fact you'll probably wouldn't even know that you are being fired at until something's hit you. Unless your opponents are using some sort of energy-emitting ("active") method of tracking your position, they would fire at you and you'd only know after you've been hit since classical information cannot travel faster than light or the laser itself.
If you have laser energy dissipating shields, then you'd see a blinding light splash across your shield when you get hit.
Now let's consider if you were in a space suit and in space and you're spectating. It's also likely that you wouldn't see much either. Lasers are monochromatic and does not scatter unless interrupted by particles. If vast stretches space, there is actually nothing there. In those regions, you wouldn't see the laser going between the ships. You will see when the laser impacts and does damage or if it is dissipated, but the whole Star Wars thing with the lasers that you can see? You wouldn't see them. If you are in a dust/gas field, then yes, the lasers will get deflected off the particles and you should see the laser. Of course laser based weapons will be less effective as it is hitting a whole bunch of stuff before it finds its way to the target. (You can think of a laser pointer at home. If you have a very clean room, no dust, then the laser point will point at whatever it is you're pointing at and you shouldn't see the beam itself. If you have dust in the room then the laser will illuminate the dust and you can make out the beam).
Continuing down the line of though, you probably wouldn't hear much if you didn't have a radio if you were in a space suit in space. Space is pretty much a vacuum and vacuums don't conduct sound unfortunately. Waves require matter to propagate (light is a special case) and sound is a wave. So without a radio, you get to watch the war in absolute silence (go watch 2001: A Space Odyssey, but ignore the orchestral accompaniment). But if you had a radio or was in a space ship, you'd hear explosions from the ship getting pummeled by laser batteries. But of course, if you were unlucky enough to get sucked out of the whole that was punched into your space ship, you'd very quickly be unable to hear anything before you died from suffocation or got incinerated by a second valley from the lasers.