Infantry Weapons by early 1941 at the latest (likely won't pay off before the Battle of France)
Advanced Tanks is the must-have. Since 1 chit (5% per turn) will take about a year to pay off, try to time said payoff to happen around March. But gotta keep ahead of the Russians...
Advanced Fighters as well-if for no other reason than to keep ahead of the Western Allies
Advanced Subs, tho this has to correlate with a major commitment to the Battle of the Atlantic (good news is that you get several freebies in 1941)
Ground Attack Weapons
Command & Control
Spying & Intelligence, again to keep ahead of the UK, tho it is likely that any advantage for either will be short-lived
Logistics: For extra HQs if nothing else; note it also gives the receiving HQ a supply boost from a linked HQ.
Now, there's some controversy about Production & Industrial tech. Germany's IT % is 15%, which is pretty significant. Production is mainly useful to minimize the costs of reinforcements, since a good chunk of your forces will likely be bought out before it has a chance to contribute. But there are those who say that the game is won or lost in Russia in 1941, and getting an extra tank or bomber for the 300 MPPs in question is a better choice. I say from experience that trying to rebuild my dinged-up forces during the early '42 lull can be costly if you don't invest in any PT.
Get Arty & Long-Range Air as well if you can spare it.
Infantry Weapons, if you plan to maintain a big push into China. They'll likely catch up with you by 1942 note (only 2 levels, which IMHO is too low)
Naval Weaponry and Warfare
Long Range Air (vital for CV vs. CV confrontations as well as air search by your Maritime bombers)
Command & Control
Any of the other Warfare techs that you can spare, but esp. Amphibious (I usually max out the chits here, note there's 5 levels)
Logistics, to defray the costs of all the amphib you will be making
Again, arguments to be made to not spring for PD or ID (or Logistics), buy more units, win the war in 1942. But there will be hundreds of MPPs to be spent rebuilding your fleet even within the first 2 years after you declare war.
Thanks for the wonderfully comprehensive and informative post. A few questions though:
*You repeatedly address the need to get ahead of the opposition in tech. Does this mean double chits on every important technology? Does the AI ever use double chits? How much of a breathing room do I have, if I neglect investing in key techs for a few turns? The issue is that I have very limited funds as Axis, and I cannot always prioritize tech over troops.
*You mention the "Battle of the Atlantic": But how realistic is it for the Axis to be competitive here? The Royal Navy is so much more powerful than the Kriegsmarine. In particular, I lack the surface combatants and Maritime Bombers. How can I successfully wage this? I'd assume I'd need an assist from the Italians, as well as finish things up before the United States concentrates its naval assets in the Atlantic? So realistically, I have to do this before 1942?
*You imply Russia can be defeated in 1941. How is this practicable? With a summer Barbarossa start, I only got to Dneiper-Daugava line in December of 1941. To even get to the outskirts of the 3 major objective Soviet cities of Leningrad, Moscow, and Stalingrad, I'd imagine you'd have to start Barbarossa in the summer of 1940 at the latest? And getting to those 3 cities is just the beginning - at least against the AI, who spawns zombie-like hordes of free units.
Is there a secret sauce I am missing?