A railgun shoots bullets - as in, projectile weapons.
Your Tesla Coil is cool for creating sparks - but what does that have to do with projectile weapons? (perhaps using magnetic fields to accelerate those pellets? If so, how would you do it in the relatively short barrel of any gun that could be mounted in or on a ship to accelerate the bullet by any significant degree? What power source would you use?)
Beam weapons - like the Doomray - may be the most viable option. After all, a single lightning strike does more damage than a single bullet.
What are those 15 credits of college going for, by the way?