In my experience as Russia, buying only infantry with occasional artillery for the first 4-8 turns depending on Germany’s moves usually works.
The best scenario for Russia is when Germany builds a large navy and tries to beat USA on their home turf (or sea :-)). This allows Russia to build without much interference. If this happens, I would recommend building inf., art., and occasional tanks/planes. The inf. and art. is cheap while still being a decent attack force and the tanks/planes gives you high hitters.
However, if Germany goes entirely your direction then prepare to buckle down and buy inf. for 6-10 rounds. If you get to a position where you begin to out build Germany on your front, then buy art. This allows you to turn all the inf. you already have into a more effective counterattacking force (combined arms). Germany also usually has more expensive units (i.e. tanks and bombers) than they do cheap units (i.e. inf. and art.). If that is the case than doing trade-offs will be in your favor. Attack their expensive units and only lose your cheap ones.
All that being said, Russia will always need Allied support to deal with a determined German invasion. Having the British build a minor IC in Persia or an American one in Norway usually works well.
Anyway, I hope that helps!