Most of it depends on specific theaters, industrial considerations, and fleet doctrine. since Man the Guns this of course assumes SP. I find trying to search for some arbitrary meta mostly useless. UK generally has two strategic goals, anti-submarine operations which could mostly done with cheap destroyers with light battery I and engine I. You can build some specialized destroyer groups with patrol groups to hunt subs. The thing you need to remember is the AI is set to medium engagement so if you have enough convoy escorts the subs will disengage against screens. For patrol groups you could get away with a single light cruiser equipped with aircraft facilities, radar, and sonar to find subs. Then you just set up a strike group of ASW destroyers. The other goal is securing the Mediterranean, there are numerous ways to accomplish this as to what is best, I'm not sure. Assuming you are using fleet in being, which I'd argue is better in this situation, you'll need a few battleships to counter their battleships, torpedo destroyers and gun heavy/light cruisers. I prefer heavy cruisers for more HP I just put a single medium battery and the rest light batteries. The general idea is to kill as many of their screens as possible till you can start targeting their capital ships. Personally, I find damaging them just as useful as sinking them, I'm assuming you just want naval superiority for amphibious invasions. Carriers are in general a mix bag for the UK, arguably more useful at the start for UK with full fighters when the Axis will usually have air superiority. As you get more air bases or bigger air bases depending on what you do, they become less useful in my opinion.
I don't know if there is an ideal composition, I generally start my convoy escorts in groups of 5 as the UK and increase their size if I fall below escort efficiency. The only hard rules I have is I aim for 6 screens per capital ship to compensate for losses or bad positioning which can increase the screen to capital ship threshold but in practice it is usually 4-5 screens per capital ship. Screens can be cheap light battery I and engine I destroyers in a pinch for battle groups but obviously not ideal. Never have more than 4 carriers operating in the same sea zones at the same time. Designing fleet subs are useful once you break screening threshold though a bit gamey. Light cruisers alone set to never engage are the best scout ships, but if you want patrol groups I personally go with a scout CL and a few destroyers with high AA, as most fleets can't catch up with them. Land base plans will support naval combat either once per battle or once per day I can't remember which. I think it's once per day, while planes on carriers will support the battle three times a day. There is a limit on how many land based planes will enter the battle based on fleet size. I can't remember the exact ratio which is why I find carriers with fighters only, more useful as the UK at the start and less useful later. Also planes when they target ships will target carriers first, and other capital ships later, leaving screens for last. Light cruisers are the best screens(particularly with some torpedoes) but take too long to build I prefer a ratio of about 25% light cruiser screens but again other factors impact that. While I do prefer heavy cruisers with guns as my screen killers, note that heavy cruisers need screens too, so light gun cruisers may be more useful if there aren't enough screens available.
Finally, as for doctrine assuming fleet in being battleships, battle cruisers, and heavy cruisers get the most gain. If you go with base strike, I'd avoid building any new battleships or battle cruisers. Carriers are your main offensive punch you just want heavy cruisers screening for carriers at that point the ratio is 1:1 but I go slightly higher 1.5:1, preferably gun heavy cruisers. If going base strike use your existing capital ships as carrier screens. Though I'd argue that base strike isn't as good for the UK but point is you could do it if you wanted to. I have, but I will say fleet in being is superior for the Atlantic and Mediterranean. Additional note for a difference between the two, fleet in being is better for convoy escort efficiency.
