Unfortunately, much of the Italian strategy is predicated on what has occurred with the UK in the Med. They get to drive that battleground in the first round with multiple options (retreat behind the Suez, attacking your BB fleet, attack your DD off of Africa and NCM to the French fleet, land in Greece just to name a few).
In general I do the following:
Buy a DD, save 2 IPC
Clean up Yugo after a German strafe for +2 IPC with an amphib with my surviving TT or two plus the units in Albania
Take S.France with 2 Inf, 2 Art for +3 IPC.
Take Kenya and join my units from Ethiopia and Somalia in Africa for +1 IPC.
Take Tunisia with my units from Libya and blitz forward the Mech and Armor from Tobruk for +1 IPC.
Lobby with the German player to allow you to take Bulgaria.
Things I MAY do:
Fly 2 Ftr, 1 Bomber and a SS and DD to kill the French Fleet off of S.France (if not, they get to convoy your territory at the end of your turn). This is mostly predicated on what happened with the UK fleet - basically if they retreated, this is why I’d make this move.
If the UK fleet exists anywhere in the Med, I send all remaining ships and my air force against it to sink it. The single most devastating thing for Italy is to allow an Allied fleet to exist in the Med. Reason? Convoy. The second you lose control of the Med, you get convoyed out of the game. Sink as many Allied ships as possible, as they are multiple turns from getting any naval reinforcements that weren’t already on the board to start the game.
Germany may be able to help clean up anything that remains depending if they are going for Moscow or London to start - just preserve your Bomber if things go sour as you’ll need it to SBR Gibraltar to deactivate the NB for when the US gets into the war.
Depending on how things go, you could end turn 1 much as 23 IPC if you gained control of the Med, with 18 IPC being a more likely outcome.
Italy 2 is even HARDER to project with so many variables, but my goal is generally to get a CV out to allow me to project force across the Med by being able to defend my Navy with 2 Ftr and a CV. This is a best case scenario, but as early as I3 you could have a DD, CV and 2 Ftr to maintain control of the Med with no more allied warships but DD sneaking up from S.Africa.
If things go well you MAY have an opportunity to get Gibraltar on I2. However, I’d recommend lobbying Germany to allow you to take Bulgaria on that first round so that you can take Greece on Italy Round 2 with a combination of Inf/Armor from Yugo, 2 Ftr and a Bomber and the Inf from Bulgaria AND NOT EMPTY ROME OF A GARRISON TO DO IT. It will set you up nicely to have a CV, DD, 2 Ftr and any remaining warships you started with to strike out for Gibraltar on Italy Round 3 to shut the Med off from any UK reinforcements (which usually means either ships or Armor are coming up from S.Africa if Germany didn’t Sea Lion). It also opens up more options for Italy in North Africa and the Middle East because you’ll have more infantry to support your advances (think free units in Iraq)
In summary:
Sink the Allied fleets by either letting them attack you (better) or you attacking them (worse, but required). Plan for losses of your ships and spend your early rounds replacing them the best you can. Project your power while setting up free IPC via NO’s (clear med, 4 points, N.Africa - in that order). Lobby Germany to let you take Bulgaria, or at worst fly a Ftr and Tac down to S.Italy on G1 and scramble them before your own if the UK attacks.
Good luck - Italy can get big fast, but is VERY susceptible to getting diced early.