I decided that I need to give a bit of depth to each weapon and explain some of the design decisions behind them. I went ahead and snagged some images from NavyWeps and Wikipedia to give examples of what I based these guns on.
15mm water cooled auto-cannon - Not yet pictured
Designed as a light AA gun of last resort, used for close in engagements and meant to have a rapid rate of fire. Nicknamed the 'Thousand' due to its 1000 RPM firing rate, the 15mm AA gun was typically mounted in pairs on a rapidly rotating, lightly armored platform. The 15mm saw widespread use in the Navy, though failed to catch on beyond naval use in the face of lower velocity, but harder hitting 20mm rounds. The 15mm auto cannon fired in rapid, long bursts meant to spray out as much mass as possible at an encroaching plane. Being such a specialized weapon, the 15mm AA gun had a short lifespan, as it did not meet army use, airforce use and was not used by the navy when anti-air guns lost prevalence.
Inspiration - Based off the MG 131, 151/15 and MG 42.
30mm auto-cannon - One of the most popular AA guns to see use in Vayiir, the 30mm gun combined a hard hitting shell with longer range than the 20mm guns of other navies, while still keeping a reasonable fire rate. Typically placed in a turret and often armored, the 30mm gun served as a medium ranged AA gun.
Inspiration - MK 103 German machine cannons. I imagine mine to fire a longer, higher velocity shell and do about 200-250 rounds per minute.
60mm AA gun - A reasonably long ranged AA gun with hard hitting characteristics. Typically laid out in a four gun armored turret and having the stopping power to hard-stop attacking aircraft. Each gun could manage roughly 80 rounds per minute and while this was noticeable lower than the 40mm guns of some other navies, the later ability to fit a proximity fuse made up for its lower fire rate.
Inspiration - An American 3" AA gun and a 40mm bofors had a baby with a lower mean fire rate, as it appears early-ish in my AU.
5" Dual Purpose gun - A heavy AA gun that was able to reload while keeping its barrel elevated, the 5" dual purpose gun often came mounted in a unique 'semi casement' turret, thus helping to move the weight of many ships lower to the water line.
Insperation