In single player, you can sink the entire Japanese navy as New Zealand just by building a single aircraft carrier and building some 1940 carrier planes for it. You can also steal the 2 English light cruisers via focus, but that is not necessary - all you really need is a single aircraft carrier, and you can destroy all AI navies in the world just with this single ship - no screens needed. You also only need to build carrier fighters. No carrier naval bombers are necessary.
In multiplayer, there are two different cases to consider -
1) the case where you are fighting next to land.
2) the case where you are fighting in the open seas, out of range of land based air.
For case 1, aircraft carriers will not sink enemy ships if you fight under enemy air superiority from land-based air. However, it can still be useful to have some carriers with carrier fighters in order to shoot down the enemy's carrier planes. Really what you want to do is to get air superiority from land-based air. But if you are forced to fight under full enemy air superiority, although your carrier planes will not attack enemy ships, they will still shoot down enemy carrier planes and thereby prevent them from bombing *your* ships. Other than aircraft carriers, the best ship for actual surface combat is always a battlecruiser (1940 model). Just spam as many of those as possible. Don't build any other types of surface ships - only battlecruisers. Some people will tell you to build things like super-heavy battleships, but this it is more efficient per IC to simply spam as many battlecruisers as possible. Some people will also try to tell you to build screens, but this is also not really necessary - you can simply get into a battle, and your battlecruisers will sink a number of enemy ships, while taking low losses themselves (they will retreat once they are damaged). Then you simply go and repair, and then once you have repaired, you get into another battle and sink more enemy ships, while again taking minimal or no losses yourself. In this way you win the battle of attrition over a series of naval battles, while taking minimal losses in each individual battle. This assumes, of course, that you don't make the mistake of attacking a *vastly* superior fleet, in which case you will lose regardless of what sorts of ships you have.
For case 2, simply spam aircraft carriers and put as many up-to-date carrier fighters on them as you can, and you will destroy everything. The more carriers you have in your carrier doomstack, the better you will do. The best fleet is something like 50 (or whatever number) of carriers and no screens. The limit of how many carriers you can have is really imposed by plane production rather than ship production.
Another thing you can do if you want is convoy raid. For this, you want up-to-date destroyers and submarines, along with ideally an aircraft carrier. Put each type of ship in the same fleet, rather than in different fleets, and this raises detection. You should also raid under land-based air superiority, which raises your detection.
