What is the most efficient (fastest) strategy to progress in heroes and generals?
---edit--- Wings of War Update: (see below for original answer) Since the this update, as well as changes made from various other updates, credit making has been shifted a bit. Please see these key notes:
1) Credits are not made from destroying tanks like they originally were. Infantry now gets credits based on experience made. So capture points, not hunting tanks.
2) Pilots now make a pretty penny. You can make a lot of money as a skilled pilot now. In a heavy fighter, I shot down 30 planes (Mostly para, probably only 12 pilots) and at the end of the hour and a half game I paid about 12,000 credits, but made nearly 30,000. I haven't played tanker in awhile but I bet they have a similar credit making system.
(updated Feb. 10th 2017) ---END edit---
Original Answer: As the other answer states, infantry is your credit making powerhouse. I have played this game for a few years now. Back in the early versions I think release X? (Xylander) you were able to make money the fastest by doing the quick skirmish battles. Now they have updated the credit system. The best way to get money is to have high rank and stay in battles long, and complete objectives. The rank you can not really control as that will come as you play more, so what you can do to help is the following:
1) Use weapons that are good without mods. For example, the bolt action rifle is really only worth using when it has the damage mods to one shot people. This means you pay to use these mods. The best money maker I have is an infantry unit with a thompson or m1/m2 carbine with no mods at all. The repair cost is much lower per game, meaning you pocket more. Starting off go with the grease gun as soon as you can unlock it. The sights are hard to use in my opinion, but I managed to get the thompson within 2 days, or about 15 games at my own personal skill level. Granted I was at sergeant rank I think? and this was back in the skirmish days.
2) For vehicles, stick with Jeep. It is much cheaper than the weasel or motorcycle and definitely cheaper than the APC. The credits you spend getting to the battle faster are worth it because you can earn more faster if you are constantly on the capture points, etc.
3) Kill high value targets. If you are infantry in a medium tank game, you can make some serious credits with a jeep and a panzerfaust. I don't recommend using the bazooka because they cost a ton to use. Use the free map panzerfausts and put the jeep upgrade on for anti armor. You get good cash destroying enemy armor. Especially heavy tanks.
4) Don't waste the grenades and other equipment unless you are using them to destroy something. The standard grenades are not pricy, but if you buy the better ones they start hitting the wallet. Only use them if they will save your life or have a high chance of netting a kill. Many players in the US faction will place their expensive land mines on the wide open bridge. This does two things. First the enemy unless they are completely oblivious will avoid them or blow them up, and two you can actually team kill because your team needs that too, which means you lose points, and that means you lose credits.
Following these few tips should help you greatly. But if you are just starting out, with low rank, and the harder weapons to use, then you just need to be a bit patient until you really start getting the stuff you want. Since the game is free to play, it may be worth making a one time investment to get some gold for the cheap to maintain good weapons like the thompson or mp40 or whatever the tier 2 submachine gun your faction has it. That way you can start making the money quicker.
Some say, it is to capture control points.
Here I will tell you how to get fast experience and money. You started as a infantry soldier, keep playing with him till you get a high rank, high rank soldiers have bigger salary. Remember not to change to another career! Why? You will earn knowledge about the game, knowledge about maps, units etc. Also having an infantry soldier gives you the ability to play almost every battle. (tank crewman and fighter pilots have longer queue times) Choose the path to unlock a sub(small) machine gun or a light machine gun, don't buy modifications in the beginning of the game. But why? Because some of them are very expensive to fix! Doing that you will be able to fill up your pockets with a lot of credits, you can hit your first million very soon. After that you acquire a new soldier that can become tank crewman, recon or pilot, without chance to becoming penniless (you have the infantryman aka "cash cow" paying the bills for other soldiers). For example your tank repair cost can raise sky high and battle profits fall, in this situation it is good to have another credit income. What gives more experience in the game? Capture a point (+100 xp per capture), Defend a point (+60 xp per kill), destroy planes, destroy tanks. This are common ones, and some others. Push with your teammates, move to the conquer area to capture this point as soon as possible (ASAP). Always, always get inside a jeep, only when there's no transport pick up a bike or a village truck. Late in your career you will probably have three or four soldiers like: Infantryman, Tank Crewman, Paratrooper and a Fighter pilot. In some matches you will be able use all of then, so you can fill in any empty slot in your team doing the difference!
Excerpt from the official New Players' Guide
Neutralizing objectives and capturing them will earn you the most XP. Also try to destroy vehicles, that will also give you some XP. Once you get enough XP you'll level up which will increase your soldiers salary. Also, the amount of time you spend in games will earn you XP. To unlock guns, grenades, cars, and other stuff. You need ribbons. By clicking on a ribbon in the menu, it'll tell you what you need to do to get it. In my experience this is the best way to progress