Germany
I had two different purchase options depending on weather or not I was attempting Sea Lion or Barbarossa. but I have since learned that Sea Lion is the best direction for Germany during the first three turns IMO.
When you consider everything like the added NO for holding the UK, $8 added income ($10 if you include Scotland), taking all of UKs money, and most importantly, taking away Britain’s ability to build units and wage war. Its a no brainer. That said, My first German purchase is an Aircraft Carrier, 1 Destroyer and a Submarine.
The most important element of a Sea Lion operation is a formidable Kriegsmarine. The western Allies may attempt taking out the German ships in round 1 with as many aircraft at their disposal, so it is imperative to protect the startup ships. an aircraft carrier instantly bolsters the fleet by adding a defense of 1@2 and 2@4 (if you land fighters which I recommend) it also gives the aircraft attacking the channel a place to land. All this for $16.
The Submarine purchase prevents the UK collecting bonus money if the Atlantic battles go bad for Germany and they end up losing all their startup subs (can’t allow the UK any extra money to build up a home defense). The Destroyer is fodder in the event that the Germans lose a cruiser and/or have a damaged battleship, its a cheap hit instead of taking off a fighter or something else major if the Allies attempt a suicide mission.
If Germany takes all the available land (France, Normandy, Yugoslavia, Bulgaria, Finland) during the first round, they should have enough $ to buy 10 transports (I suggest buying all ten even if the job can be done with less, they will come in handy during the rest of the game).
Japan
I buy 2 Transports and 1 Cruiser J1. I am currently experimenting with a strategy where I go full out on Calcutta abandoning the China coast for the same money south. eventually I will buy a minor IC in Malaya and after the capture of India I will create an outpost that can threaten ANZAC. The problem I am having is, defending the home sea zone because my attacking fleet in the south (which needs to be as large as possible, especially if the UK diverts its Mediterranean fleet) always gets cut off by a huge US fleet parked in the Caroline Islands.
Italy
My first few rounds, I purchase 1 transport and 1 infantry. I than use the rest of the game landing troops on every coast in every direction. Italy is easy to play because the goal is never in doubt, just collect all the Italian NOs.