We have already discusses missiles/torpedos. I am also envisioning large caliber naval rifles being in fashion. Even back in the last century they could achieve muzzle velocities beyond 700 m/s. (The nuclear version of the shells for the Iowa class could reach 820 m/s!). In the vacuum of space there is nothing to slow down your shells, no gravity to cause bullet drop, and no curvature of the Earth limiting line of sight.
A computer to work out firing trajectories was well within mid-20th century technology. I suspect they would be operating down at the smaller calibers of naval rifles. While a larger shell can carry more explosives, and more kinetic energy, it leaves the barrel with a lower muzzle velocity.
I discovered in my research on point defense weapons that 20mm cannons are used almost exclusively for modern fighter cannons. They have the perfect blend of muzzle velocity, stopping power, and capacity for explosives.
The GAU-8 (at 30mm) was designed for stopping tanks, not aircraft, thus why they favored a larger shell. Larger rounds can penetrate more armor. Smaller rounds can fly faster. The exact size of shell selected for the main guns on a warship would depend on the thickness of the armor on the enemy they are trying to defeat.
Sublight does not have force fields. It will NEVER have force fields. They only exist in science fiction because model makers didn't want to have to put battle damage on the hero ship for TV shows. Syndicated TV meant that episodes would air in random order, so trying to keep the progressive destruction and repair patches consistent would be a fool's errand, anyway.