For purely defensive purposes, buying infantry cannot be beat. When you can swap in an offensive piece (artillery or tank) without decreasing the number of units you’re putting on the board, this is well-advised. The relative cost of units and their defending capability seems to be balanced such that quantity is quality.
For example, Russia starts the '41 version with 30 IPC. For that money you can buy 10 inf OR 8 inf and a tank, etc, etc… OR 3 fighters. If you benchmark every 30IPC purchasing combination against an attacking force of 4inf and 5 tanks (nearly a 50/50 battle with about a 2% chance of mutually assured destruction if you purchased 10 inf), the results are telling:
10 inf - 49% chance of winning [2 * 10 = 20 hit points or 20/6 = 3.3 average hits]
8 inf, 1 tank - 38% chance of winning [2 * 8 + 1 *3 = 19 hit points or 19/6 = 3.2 average hits]
5 inf, 1 tank, 1 fighter - 16% chance of winning [5 * 2 + 1 * 3 + 1 * 4 = 17 or 17/6 = 2.8 average hits]
3 fighters - 0.02% chance of winning [3 * 4 = 12 points or 12/6 = 2 average hits]
No combination of possible purchases perform better than 10 inf in this scenario.
However, when playing against a German Goering that likes to over-extend poorly defended fighters or bombers to gain a couple of IPCs, it’s nice to have the offensive capability to wipe them off the board. I have found this is best accomplished by pushing infantry forward (protecting your offensive pieces from overwhelming counter-attack) and keeping a mix of infantry, artillery and tanks within striking distance of the front line.
For offensive purposes, the best mix of units for the same 30 IPCs, baselined to a 50/50 battle of your 10 infantry against a defending 6inf + 1 artillery (approximately 1% chance of a draw):
10 inf - 50% [10 * 1 = 10 points or 10/6 = 1.7 average hits]
8 inf, 1 tank - 60% [8 * 1 + 1 * 3 = 11 points or 11/6 = 1.8 average hits]
6 inf, 3 art - 81% [3 * 1 + (3 + 3) * 2 = 15 points or 15/6 = 2.5 average hits]
5 inf, 1 tank, 1 ftr - 42% [5 * 1 + 1 * 3 + 1 * 3 = 11 points or 11/6 = 1.8 average hits]
3 ftr - 0% [3 * 3 = 9 points or 9/6 = 1.5 average hits]
For purely offensive considerations, the optimum combination of units in this scenario is 6 inf and 3 art at 81% chance of victory with 4 inf, 2 art and 2 tanks in close second at 80%. No combination of purchases which include a fighter score better than 53% (4 inf, 2 art and 1 fighter happens to be the specific combination in this case). Again, there appears to be a quality in quantity that supersedes just quality. It may go without stating, but if attacking a territory with an AA gun, the numbers will be even worse for the fighter purchases.
For the two scenarios above, the most balanced purchase (averaging the %won for each purchase in its offensive capacity and defensive capacity) is 7 inf, 1 art and 1 tank. This particular purchase is the second best defensive purchase (next to 10 inf) and only 4% less potent than the best offensive purchase (6 inf and 3 art).
I’m not against fighters or bombers, they certainly have their place I just haven’t found justification for purchasing them when playing as Russia (or Germany for that matter) - especially in the early rounds.
Similar conclusion are drawn with respect to naval units - more cost-effective units (subs and especially destroyers) are typically better than fewer high-powered units (battleships and especially cruisers).
Excepting special circumstances (such as no time to get infantry to a developing hot-spot on the map or needing to sandbag funds for a massive naval build against enemies squatting in your sea-zone) a good rule of thumb seems to be to maximize the number of attack/defend points your are bringing to the board, first, and spread over as many units as possible, second.