Whenever I'm Italy, I reorganize my starting navy into the 2nd-4th fleets. The 1st fleet being a flotilla of 30 level 4 vessels.
2nd fleet consists of all vessels being level 3 and above plus the 4 BB's It is a 20 flotilla fleet that I suppliment with one level 4 BB, 1 4CA, and 4 4DDs. The 6 CLs and 4 CAs are level 3.
Third fleet consists of remaining CAs, CLs, and DDs, all of which must be at least level 2. I had this to total 20 including one extra CA that was level 4. I also suplemented with some elvel 4 DDs.
Fourth fleet consists of the level 1 ships meant entirely to pin down enemy vessels for a strike by the powerful ones.
I generally prioritize research on my navy. Since most of the research to level 4 is done it doesn't take too long and you can still get a good army. Although I always use carriers just because of my belief (history showed it to be true) that CV's own the open waters, it seems not bothering with them is good enough (which I do if the country is not that strong in terms of naval research and relatively low on IC) If I intend on a long term war that lasts well into the 50's (ex. German domination over the world) then I continue to research to the nuclear level and make them in time for 1945. Otherwise I delay updating my fleet until I've really given the allies or whatever enemy I'm going up against a real pounding as level 4 fleets are usually good enough until 1945.
1st fleet:
3 level 4 BB
3 level 4 CV
8 level 4 CA
16 level 4 DD
I always invade Spain before the civil war for a lot of extra IC, resources, and easy takeover of Gibraltar. I rush Suez and the lockout of the Med is complete. Just before I DoW the Uk (if I decide to, sometimes I let Germany duke it out alone wqith the allies and help them vs Russia for the massive resource deposits in the south) I place all the troops I need where I need so even if I were to lose all my transports, it would not be a major strategic loss until I can wipe out the RN.
Also you want to concentrate on 3 types of vessels or so. BCs for example aren't really needed when you start off with level 4 BB already researched, etc. Depends on your preference.
Whatever you do, I highly recommedning DoWing Spain before the civil war. It gives yuou the IC you need for a 5th tech team and makes the whole domination of the Med thing so much easier.