In the early game it’s infantry, infantry, infantry.
Usually, the best thing to do is hit Finland right off. They’re not that strong initially. Taking (and holding) the border territories will alleviate pressure on the Soviets when Germany attacks.
Going into Iran is a good idea too.
If Germany doesn’t, the Soviets should take the Baltic States. Don’t neglect Eastern Poland Either (unless you want to leave the Poles as a pain in the $$$ buffer for the Germans. The extra income won’t be noticed anyway.
Back off from all border territories from the Baltic on down. Leave infantry screens of one division for each border territory. This creates dead zones and neutralizes Germany’s one territory sneak attack. Let them swing at wind as much as possible.
Make sure Leningrad has plenty of infantry. Use the fortifications their to your advantage.
Use the cities of Smolensk, Kiev, and Stalingrad as strong points and bases to launch counter attacks on German spearheads. Counter-attack aggressively. Add planes when possible to augment your offensive strength and to give you the range to attack German advances across the front.
Pull back from the Japanese border (again, leave a screen). A couple of tanks and three+ infantry in Novosibirsk (arty/mech combo might be hand here too) is not a bad idea to keep the Japanese guessing.
Defend Karelia and Moscow aggressively.
Roll them dice for your full income like your life depends on it (because it just may!).
When the Nazis come calling, send your navy to help the UK and/or raid the Germans in the Baltic.
Don’t just give up territory after the initial attacks. Fight back as hard and as often as possible. Maintain those dead zones. Push into the Middle East and North Africa from Iran if you can. Threaten Cairo. Hastle the Italians.
Don’t forget about the Guards and KVs when the income comes up. Use them especially to defend the VCs and Karelia.
Try using HBG’s minefields (land and sea) and rules as well.