There are quite a few ways to go-
The first question is, do you want to protect your Baltic fleet? If so you should invest in navy on the first turn. Whether that’s a carrier, or two transports is up to you, but those are widely regarded as the two best naval purchases. The two transports means you’re probably going to have to buy a carrier on round 2.
A non-naval purchase is best, in my opinion, if centered around infantry. 10 of them is pretty solid, along with 2 armor, or a fighter etc.
In a non-bid game, it’s incredibly important to take out Egypt early on (important in a bid game as well, just a different way to accomplish). Take an infantry and armor from S Europe, and drop them off in Egypt. Your Battleship will have to take care of the destroyer parked there. Bring a bomber and fighter as well, and the forces from Libya. You should take it with 2 armor remaining.
Take your sub in SZ 8 and hit the British Battleship near Gibraltar, along with 3-4 fighters (the more the better). You can land them all in France to hold down your flank, along with 3-4 infantry and an AA gun, maybe an armor.
On the Eastern Front with Russia, you’ll have to respond to what Russia has done to you. Gaining the initiative on the front is a huge factor. Karelia is a key spot, but so is W Russia (for Russia). Whoever gains the upper hand and can stack in those territories will have an edge in the economic battle. Be careful about being too aggressive unless you can take out alot of Russian hardware- you can rebuild tanks and artillery more quickly than Russia can.
As a general rule, try to keep your airforce where it can threaten the land and sea in as wide an arc as possible. German fighters are extremely important, so try not to use them up unless a great opportunity comes to devastate allied shipping.
Be careful about dumping large amounts of economy in Africa. Try to keep in mind how many IPCs you’re gaining vs. how many you’re spending to keep it. The ebb and flow of most games with experienced players sees a surge in Africa for Germany followed by a quick (3-4 round) cleanup by the allies, sooner if they’re determined to get you out. You can coordinate with Japan to have them take over the as the muscle in Africa as soon as they can marshal the forces to swing in that direction.
If the allies all come after Germany then infantry will be your best friend. You can buy 10 per round deep into the game, and if your opponents are buying more expensive units you’ll eventually see an opportunity emerge. Your job in that case will be to hold down the fort and threaten Russia just enough to allow Japan to do the dirty work.
I might be preaching to the choir, since you have experience in the original, but I hope this gets you thinking a little bit. Above all else, have fun and try things out.