Superheavy: The only calibers I use in this grouping are 17" occasionally and 18" rarely. The computer doesn't build anything that I feel that I need such guns to defeat, and even the 17" and 18" guns tend to be borderline-impractical on ships that I'm actually willing to pay for - all the more so considering that I can usually build carriers and often have at least halfway decent strike aircraft by the time I have any decent-quality guns heavier than 16".
Heavy: 11" is probably the caliber I least often use, because I've never been particularly impressed with the heavy-gun CAs that I've built - whether early-game Tsukuba-type first class cruisers or mid-/late-game Deutschland-type heavy cruisers - and unless you're Germany, Austria-Hungary, or Japan you're almost always going to have a better alternative for use by capital ships against capital ships available domestically, with only the occasional instances where you develop something like an 11"/Q1 before 12"/Q0 or anything heavier offering anything like a counterexample. Additionally, as the lightest available heavy gun, it's also perhaps the most severely limited by early-game constraints on the number of main battery guns you can install on the ship, because you can't offset a weight-of-fire disadvantage with volume of fire when you can only fit six or eight guns on the ship in the first place and a 1" smaller heavy gun is neither enough lighter to be the difference between six or seven or eight guns nor endowed with a notably-higher rate of fire.
Beyond that, 11", 12", and probably even 13" guns aren't really in the same league as 14", 15", and 16" guns, especially when the lighter guns lack a qualitative advantage - just look over the range and penetration data from the 1909 save state of my Great Britain AAR game:
or the range and penetration data from the 1964 save state of a USA game that I finished a while back:
and look at the differences in range and armor peneration (granted, the 11" guns in the 1909 dataset are further disadvantaged since they're Q- guns being compared against 12"/Q0, 14"/Q0, 15"/Q-, and 16"/Q- guns, the latter three being fairly advanced guns for 1909 and the former still being more advanced than the legacy-tech 11"/Q-). But, hey, at least 11"/Q- is arguably superior to 13"/Q-2, inasmuch as it has a greater maximum range and only slightly worse armor penetration while having a sufficiently lower tonnage cost to possibly fit a couple more guns without sacrificing much.
Mind you, I tend to prefer 15" and 16" guns for superdreadnoughts and fast battleships, so 13" and to a lesser extent 14" guns somewhat often find themselves used only on transitional designs - they're usually the first available battleship guns that are better than 12" but they're also not really at the point where I'm happy to call them good enough for all future designs (13" more so than 14"), so they tend to get stuck on the transitional designs between the early dreadnoughts and the late superdreadnoughts and fast battleships and may be passed over entirely
Medium: Personally, I think you should distinguish between the first class/heavy cruiser main battery guns (typically 7"-10" but sometimes also 6" and, on player designs, 11" or 12") and the second class/light cruiser main battery guns (5" and 6", maybe also 4"), but up to you.
- 5" is my preferred capital ship secondary battery from the dawn of the dreadnought period onwards, and is also my preferred main battery for CVs (if the DP version is available) and large destroyers. Sometimes chosen for CL main batteries, particularly later in the game as airpower starts becoming a larger concern.
- 6" tends to be my preferred CL main battery and is often used in predreadnought battleship secondary batteries. Also tends to be my caliber of choice for CA-type second class cruiser (~6,000t early-game CA) main batteries.
- 7" sometimes shows up as a predreadnought battleship secondary battery or for large second class/small first class cruisers (~6,000-8000t early-game CLs with 7" or 8" guns, similarly-sized CAs). I've also recently been experimenting with them as main batteries on midsize first class cruisers (~10,000t early-game CAs), with mixed results.
- 8" is probably the caliber I most often use for the intermediate battery on semidreadnoughts and, as with 7" guns, sometimes gets used on large second class/small first class cruisers. Sometimes gets used as a main battery on heavy cruisers, but I tend not to build many of them.
- 9" is probably the caliber I use most often on midsize first class cruisers and is sometimes used for the intermediate battery of a semidreadnought or on large first class cruisers (~12,000t+ early-game CAs), especially if it's better than my 10" gun. Occasionally gets used as a main battery armament on heavy cruisers, but I tend not to build many of them.
- 10" is probably the caliber I use most often on large first class cruisers and is sometimes used for the intermediate battery of a semidreadnought or on midsize first class cruisers. Occasionally gets used as a main battery armament on heavy cruisers, but I tend not to build many of them.
Overall, 7" and 8" are probably the calibers in this group that I least often use, with 8" probably being used very slightly more often. That said, if you discounted legacy and early-game CAs, 9" and 10" probably wouldn't be doing any better. 5", meanwhile, is probably my most widely-used gun, especially after the dawn of the dreadnought ear.
Light:
- 4" is my preferred tertiary gun on predreadnought battleships, DP secondary gun on heavy cruisers, and DP main gun on CVLs, second choice (after 5" DP) for CV main and fast battleship DP secondary guns. Also normally the primary armament of 700-1,000t DDs, and is sometimes selected as the armament for colonial/raiding cruisers, corvettes, and AMCs.
- 3" tends to be my choice for the main battery of 600-700t torpedo boats and sub-700t torpedo boat destroyers, and sometimes for the main battery of 700t torpedo boats and torpedo boat destroyers. Occasionally selected as the main or secondary battery on corvettes, sometimes shows up as the DP battery on CVLs and ships that didn't originally carry a DP battery.
- 2" tends to show up on 500t torpedo boats and as a secondary gun for early-game torpedo boat destroyers, mostly because 2" guns are cheaper and lighter than 3" guns and I don't expect much out of early-game DDs in a gunfight even when I give them more useful gun armaments. Also quite possibly the best gun in the game for any design intended for use in a role where cost is a much more important consideration than combat effectiveness - ASW/minesweeping/TP corvettes and destroyers, for example - though the savings are unlikely to amount to much because it's not like a couple 3" or 4" guns are much more expensive in the grand scheme of things.
Of these, I use 4" significantly more often and more widely than either of the others, and probably use 2" about as often as 3" - mostly because I typically go with either 2" / 3" / 4" main batteries on 500t (legacy) / 600t (second-generation) / 700t (third-generation) torpedo boats or (3" or 4")+2" / (4" or 3")+(2" or 3") / 4"+3" main+secondary batteries on 500t / 600t / 700t torpedo boat destroyers and then shift to a 'modern' destroyer (torpedo boat / torpedo boat destroyer hybrid) with a 4" main battery and no secondaries at 900 tons while rarely using 2" or 3" guns on anything else of any particular relevance.
Have fun trying a game without DP guns
Seriously, I think you need to ignore the 2" calibre for this to work...
In all honestly, I probably use 2" guns about as much as I use 3" guns - I prefer 4" guns to 3" guns for light ship secondary, heavy ship tertiary, and DP batteries; my legacy DD is frequently a six-tube torpedo boat with 2" popguns because because the 3" version either drops a knot or carries only one gun (usually goes to 3" on the 600t and either 4" or additional 3" on the 700t versions; 900t and heavier DDs use 4" or 5" guns and don't normally have secondary batteries); and cheap corvettes/AMCs somewhat often carry 2" guns because they're cheaper than 3" guns and it's not like I'm building them for their combat prowess.
Also, technically, any of the heavier guns can be DP guns with the tech for heavy AA shells, though the nominal date of development for those (1942) is a little on the late side and the tech can be skipped, so even if unit24 ends up using nothing between 2" and 7"+ it's not quite guaranteed that he or she won't have any DP-capable guns.