Here's a bunch of ideas that work for me or that I've thought of trying but haven't just yet....
Use the first few years building up your IC. You can gain the IC needed to get the last tech team just by building it I've found. It takes about three runs of what IC you can spare to do it. You have to trade enough supply for the resources to run at max capacity though.
Also, I don't know if it's the best idea in MP, but you can always pull all your infantry home, group them in one huge army, give them a logistical leader, and install all the ministers they have that give them reduced supply consumption. I guess you could also leave larger seperate armies because Italy has to have more then one logistics wizard. But, if you know the allies aren't going to attack you in june of 36, then it'd be safe to do.
I'd also ally with Germany as soon as possible, and trade techs. Figure out what your teams can accel at researching, and tell the German player that you'll take that path. Then, Germany can concentrate on a different research and you'll trade him the prints from that path allowing you both to accelerate your research. Granted, you'll get the better deal because Germany can give you more prints, but it's good to make it helpful for him to do so. This way you aren't both researching infantry or motorized at the same time. It always sucks to be offered a blueprint when you are at 95% research!
Also, on top of that, ask Germany to do trades for you. Italy seems to get worse trades then Germany does from most nations. Not sure why, but you'd probably be better off trading him the supplies and seeing what he can get for you.
If Germany doesn't mind, I'd get out of the Alliance before war starts. This allows you to get all the benifits of the alliance up until 39, but not go to war with the allies until YOU choose to. Gives you a little more time to prepare, and will probably tick off the players of the allies because most of them won't be able to attack you now
You can also liberate Lybia and Somalia with no real loss to you. Both have no strategic value and are better off as puppets because then they gain IC. You might also get some techs out of them too
As for who to attack? You can basically head straight east around the coast of the Med. and annex all in your wake. I'd either stop at Turkey, or be prepared for a possible Russian attack. Take Istanbul and the other side of the canal and wait for a peace offer. Perhaps take some more territory, but leave anything north east of the capital. When they offer peace, you'll have a nice little chunk of Turkey, but what's left will stand between you and the Soviets.
Italy can isolate itself pretty well, only having two or three provinces of the mainland connecting to France. If you have no problem loosing Ethiopia, you can fight the Allies from Fortress Rome. Naval bomb any fleets in the med (after having the latest and greatest model and doctrines..not a bad thing for you to research as the levels are low and then trade with Germany as stated above!), take the islands that you can,
and do assults into Africa.
If you regularly harrass the Brits in Africa, they wont be able to pull those armies back to defend the main islands. But, in the begining if he sees you pulling your forces back, and then sees you break the alliance with Germany, he might very well think you won't be much of a challenge and pull a lot of his forces out of Africa. This will allow you to maybe trick him and run rampant there once you rejoin the Axis after war starts.
Last idea, when Vichy fires, Vichy is always a nice target
Joshua