All slots filled on DD with as many DP's as you can. As per the cruisers I meant the light cruiser batteries, I was unclear. I typically use the Atlantic fleet designer or japans battlefleet designer. I typically fill every slot on every ship with something if I can.
DP DD batteries are 300 IC and 1 steel each. Using a DD2 with 3 such batteries is going to cost around 1520 IC and 5 steel per yard. DD3 with 4 batteries would be 1900 IC and 7 steel per yard. That doesn't include radar, sonar, FCS, torpedoes, AA, or potentially higher level engines. Those are super expensive for DD that have no armor and only 40 or 50 HP, while only offering 9 or 12 LA/AA at 2 piercing.
Anyway, as for
My preferred fleet would be Gunboats destroyers with DP guns, 3-5 SHBB with either all heavy guns(if I know someone else is building them) or all heavy guns with as many DP secondaries as I can. 2-5 carriers(either all fighters to counter other carriers, 50/50, or 10-20 bombers per carrier with the rest being fighters depending on the situation), and armored light cruisers with either all light batteries or a mix of them, and DP guns to save cost(I often convert heavy cruisers into lights). Fleet in being with iron sides admiral. Typically with naval advisors selected and as much naval tech and radar as I can.
How many of each type of screen are you expecting to have? So far you're saying you have 2-5 carriers, 3-5 SHBB, and an unspecified number of screens split between armored CL and gunboat DD.
You've also jumped between the different nations a lot. You're talking about American SS spam, Japanese battle fleet designer, and Italian research boosts.
I can't see how as an Axis major you could hide your navy until '41, and still have been able to do conquer anything like the Axis would. Italy needs to control the med, usually by controlling Afrika. You can't really control Afrika is the Allies are raiding your convoys trying to ship them supplies. Japan would need to use their navy if they planned on cutting off allied rubber from the east indies/malaya, or send supplies to china to take the Raj. Germany is going to need to use its navy to invade norway, unless it goes through sweden. Neve rmind all of the lend lease and trade raiding you could be doing to limit the allies ability to cooperate. If the big war is projected to start in '39, waiting until '41 to use anything larger than a submarine is giving the enemy a full 2 years to do as they please, unmolested.
How do you expect us to believe you have up to 5 SHBB and carriers, and untold swarms of armored cruisers and gun-laden DD? Fair enough you might have tech rushed, and spammed yards from day 1 or something, but where might you be getting the steel for all those ships? 50 or 70 steel for a single line of DDs is a lot of steel, and you're going to be sinking even more than that into the CL, BB, and CV lines.
So, please stop talking so vaguely. Please, give us some more concrete timelines, designs, and numbers.