This is a good strategy question. When playing the Germans/Americans I have found that Advanced medium tanks quite effective in early phases of a match.
You only need a couple of recon. Keep them in forests beyond bridges/choke points you control. AA is critical, but keep them a little back from tanks to avoid enemy fire. But not too far, or they can't provide AA cover. I have also found using upgraded foot soldiers very effective in groups of 3 against tanks and heavy machinery, providing they're in fortified locations. They get a big bonus for ambushing and also a defense bonus. That's a good cheap way to hold choke points around towns or roads that go through forests.
Anti-tanks are limited because they are vulnerable to all sorts of attack. I rarely use them, but that's not to say they're ineffective. They can add punch to a squadron of tanks or infantry you've based in a town. So, use them in fortified locations, (ie Towns, and Forests that have roads passing through them).
Advanced Medium Tanks (ie Upgraded Medium Tanks) are almost as effective as Heavy tanks but usually cheaper. So my tendancy is to have about 80% medium/20% heavy tanks.
So, in summary. Use AA but not too close to front line. Advanced Medium Tanks are cheaper and almost as effective as heavy tanks. Weight your mix of medium/heavy tanks 80/20. You only need a few recon but position them for advance warning. (Upgraded) soldiers are great to hold towns and choke points. Finally Heavy Artillery, can be good depending on the nation you play. Upgraded artillery should always have AA cover. I dont find mobile artillery that helpful.
About resourcing. You mentioned that you have a cash shortage. My strategy is to get the first couple of the nearby supply depots, and then use a "blitz" ruse to speed up the initial cash flow. Then go further abroad to the map edges and get other depots. Again use a "Blitz" to speed construction and supply truck movement when you have a surplus of Ruse cards. If cashflow is good, and the depots are far, create a secondary HQ. This is better than using Blitz to bring trucks in from far away, and it will save RUSE cards.
If you have a big attack coming in, and providing it's not a RUSE from them, use a "Fake assault" RUSE elsewhere on the map to draw them off.