Plains and other open spaces
Most often you will find yourself fighting over an open patch of land, where reinforcements can arrive from practically any direction. In open fields like this, the most importent unit is the rifleman. They should be quite neumerous, as they are usually spread out and losing sight over a patch of land will allow the enemy to position his heavier weapons closer.
Other things to be weary of are penetrative attacks with transports or light and medium tanks. Since infantry is usually spaced out, the risk of running into grenades is very low and faster units tend to take advantage of this. Givin the battle is taking place in an open space, moving around the area of combat is extreamly easy. Preventing the enemy from getting good attack angles is key.
The best unit composition in this situation is very simple: huge amounts of infantry and some sort of anti-armor solution. As the game progresses, you will need more infantry and heavier anti-armor, but the general idea stays the same.
For examples of plains, you can check out the map "titan" for Spring:1944, most notably the center location. Having full information about that area will give you a definate advantage, but spreading infantry so thin will not make them better at fighting, hence the rather unorthodox unit composition.