Well, my usual approach to naval warfare is rather a bit boring (especially because I do it more or less the same with whatever country I am playing):
# upgrade all old Trans, CLs and CAs to CVLs
# upgrade those old BB and BC to CVs
=> those old ships are too slow with not enough range (not shooting far enough nor can they sail longer distances) and usually they just cripple the newer ships because the capital ship with the shortest firerange dictates what distance your admiral is aiming for in a seabattle
If there aren't enough old ships, I build more transporters and upgrade some of them to CVLs as well. The carrier air groups, LCAGs for CVLs or CAGs for CVs, need to be built additonally.
So with this fine armada of carriers you need to build fitting escorts: destroyers. Not only that they are cheapest and fastest to build, they also cover the worst weakness of carriers and that's U-boats. Really good is the 1937 semi-modern destroyer which I usually massbuild (in my present game I have 9 parallel build running... shortest to build means it takes still long). If I expect trouble before 1939, there is no other way but to already build the 1933 improved destroyer.
In the long run it is excellent if you manage to outfit your destroyers with ASW and your capitals with anti-air.
A CVL-DD fleet is a fine general fleet, good for escorting transports and keeping enemies at bay as well as fighting other capital fleets directly.
BUT:
1) As long as your carrier fleets can keep the distance to the British heavy pounders, everything is fine. But one battle in which the Royal Navy manages to surprise you and is in best shooting distance and they'll sink or severly damage your ships.
2) Most likely you won't have them in abundance and any losses take long to replace. And even if your CVLs/CVs are only damaged, it takes an eternity to get them repaired.
And gone is your best ability to escort your transporters. Unfortunate.
Thus I try to keep my CVL-fleet out of intentional trouble (meaning: not hunting British BBs with purpose). The search&destroy mission I delegate to fleets of heavy submarines. Even cheaper than DDs, faster to build, also faster to repair. And if you loose 3 U-boats while killing 1 BB... quite a bargain. Depending on version and mod you are playing, those heavy subs come as early as 1924 or 1933. I have usually 6 parallel builds queued with floatplanes attached and try to have 24 or more when the spectacle starts. After a few batttles, usually half of them are in port for repairs. For BB/CV hunting I use packs of 6, for the occasional convoy hunting packs of 3. Make sure to switch your hunting ground to a different area after a success, since NAV-bombers and DDs will be sent out to hunt your U-boats.
Usually I feel tempted to build also fine fast new CLs... but I can resist. One has to concentrate and to focus. BBs and BCs are shiny and glamarous... for the old big imperialistic powers to show off while the hungry newcomers for worlddominance know that the true power will be in carriers and U-boats.
So fine, so far. The problem to make it work are the naval doctrines.
Look at the overview in the tech section: Naval Positioning.
Basically those values show how good your admirals can get your fleet into the right position to shoot at the enemy fleet at YOUR best distance and make your shots actually count and not go astray or at the wrong ships. In battle your positioning tables run vs the enemy positioning tables. That's quite simplified but the gist.
For Germany it is easy and possible to get their U-boats to a value beyond 100 because they have good tech-teams specialized in researching U-boat doctrines and naval interdiction doctrines. But they utterly suck with carriers, so it takes looong time to research those. But IMHO and experience the CVL/DD combo is that strong that it is still better than going for BC/CA for what the German Kriegsmarine and techteams were outfitted. I can't remember how it is for Italy, sorry. But if CVL-fleets can be made feasable for Germany, it should be possible for every nation.
Add on:
You asked for fleet warfare. But some additional hints specifically for Italy:
Gibraltar and Suez are the most intersting regions. Splendid if you get both, but one is also quite good.
With all the coastlines the Mediterranean is excellent NAV-bomber area.