I haven't explored animation much beyond the odd walk animation. The setup in 3ds max is pretty intuitive, so I think I might have a solution for you.
Looking at the object creation panel, click on geometry (where you make boxes) then click on drop down menu (standard primitives, extended, etc), then select particle systems. Superspray seems like the kind of thing you'd want. You make it with a click and a drag. There are a bunch of settings that you can play with, and it looks promising. Just position the Superspray at the tip of your laser guns, then link the Superspray to your ship (use your schematic view to see the setup).
A couple of things I've noticed right off the bat:
-The particles have to travel faster than your ship, or they'll fall behind. You can change that under the "particle generation" drop down on the right hand side.
-There's a feature in the "particle feature" drop down that lets you use instanced geometry. I think that means you can make a little model of the laser bolt and then select that as the object to get shot out.
-There's a material feature as well, so that could get you the glow for your lasers. I don't know what impact a bunch of light-emitting particles would have on the render time, but it would look cool.
Hope this helps!
Edit: To turn it off and on, go into your curve editor and have the birthrate set to zero. Then at the moment you want to shoot the guns, make the birthrate jump to whatever you want, then back down to zero. You'd use the stepped tangent for this ( the button third from the right in your tangent buttons in the curve editor)