For income, sell every piece of alien technology you find. Keep only one sample of each for yourself to research. That's been my main source of income aside from the monthly funding. Terran weaponry is, if anything, more effective than the plasma weapons the aliens start with, so they're not worth your time to research at first anyway. An exception might be the plasma grenades, since you can build plasma rounds for the grenade launchers.
For the world happiness, sell every crashed UFO you recover. Only keep the intact ones, and then only one each of the scouts and fighters. Fill the rest of your UFO yard slots with intact Harvesters. When you sell the UFO's, sell them to the most unhappy nation. It won't provide a huge boost in their happiness, but it can keep them for a few months. Long enough to get a new base built in their territory, anyway. Once you have a base built in their territory, shoot down every UFO that comes into radar range. Even if you don't recover any of them, the aliens won't complete any missions in that territory, meaning the host nations happiness will degrade very slowly.
Those are really your only two options. The base you start the game with is NOT enough to cover the entire planet and keep the funding coming in. As soon as you can get the money, you need to start building combat bases on other continents (Either using some of your starting cash at the very beginning of the game or at the start of April).
