Italy’s job is threefold:
1: Keep the UK spending to crush Italy
2: Assist in Russia
3: Lure the US Fleet past Gib and into the Med
With that being said, the Italian Navy is important to protect, requiring a DD to be purchased in Round 1. This will draw more UK attention to the Med, which gives Germany more breathing room to advance on Moscow. Provided your fleet was not decimated in SZ97, ferry units into Yugo with the TT and at least 1 Armor, possibly 2.
Assisting with Russia being your second goal pretty much requires that Italy activates Bulgaria on Round 1 and Italy either reinforcing the German Flank in Romania on I2 or if there is no immediate threat, clearing out Greece before the Brits activate it. If Italy purchases a Bomber on Round 2, it puts 2 Bombers and somewhere in the range of 6-8 Inf plus 2 Armor in range of Eastern Poland, or Bess. You even have a shot to can open Western Ukraine at this point, or if Russia is really incompetent, Ukraine MAY be open via an Armor Blitz (provided 2 Armor went into Yugo on Round 1, and reinforced Romania on I2.) In any case, Italy can stand to gain some IPC and really create problems on the German Southern Flank in Russia.
As for the last goal for Italy, you need to continue to engage the UK into the Med through the time the US enters the war. Usually this requires naval investments, I prefer to try to get at least 1 DD in every round. At some point you’ll need to redirect your Bombers back to Rome / Southern France. You’re goal is to force the Allies to defend SZ91 and interrupt the US TT rotation. You need to be very opportunistic here and wait for the Allies to expose TT as lightly defended. This doesn’t always happen, but it is devastating when it does and you can fly 2-3 Bombers and a send a few SS to potentially sink the TT rotation and buy breathing room. If this doesn’t look like it could happen, you just have to turtle up and encourage the US to land on Rome and not Normandy or S.France. The whole goal being to keep the US fleet in the Med and out of reinforcement for multiple turns outside of the 3 units it can place on whatever complex it takes.