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Good options

1. At the very start your best bet is fighting bandits/looters and selling their equipment. You will probably even be able to fight the smallest parties all alone by kiting them with a crossbow on horseback. However, the sums you get are very small compared to what you will be able to receive later.
2. When you get some combat stats to win the tournaments, some money to risk on bets etc, you may try your luck. I don't suggest going higher than 4 at any single combat skill because you will need those valuable points for Charisma to increase party size and decrease party wages and Intelligence to train soldiers quickly and persuade lords to join you. Tournaments will get you both money and renown, and the rate will be high at the beginning. However, the bonuses will quickly diminish if you become a famous and renowned fighter.
3. Quests -- when you are more or less established, but not a steamroller to everything yet. This is most important because you get reputation with quest givers, especially villages. Choose which quests to do and which to ignore -- for example, I don't like quests about interfering in a conflict unless you can settle it, because you lose in total. I don't take herd quests either, because it's very hard to move it in vanilla, etc.
4. Dyeworks in every town. Just steady income. Takes some time to pay off, but once you get some extra money, put it here. Begin with the cities with which you don't plan to have a war soon, otherwise, your income will be arrested and never pay off. :)
5. Get towns. One town gives you around 10 thousand a week, two towns yield around 15 thousand. Do not accept castles or villages: they give very little income, but game mechanics punish you for having too many fiefs.

Not-so-good options

1. Trading is an option if you have a trader in your party, but for me it becomes boring quickly, plus you probably need skill points for something better for end-game than Trade. The biggest problem, however, is that merchants have very limited amounts of money, so the scale of your trade factory is going to be very limited. Once you will find yourself in a situation that you just can't sell all the things you bought where the price is highest... So don't go for it unless you roleplay a trader.
2. Raiding villages. Yes, if you have a good looter in your party, the amount of money you get is tremendous. Or it may seem so. But: 1) You will conquer this land at some point, and the economy will be ruined. 2) Your relationships with the village, its lord, and the faction will be ruined 3) Your honor will drop, which you will need later. So don't do it unless you roleplay a looter.
3. Looting -- when you are established already. It fills your inventory with useless things and slows down your army. The opportunity cost is just too high.