What Is The Most Effective Way To Earn Money Without Raiding Villages?

While I agree that tournaments one of the fastest ways of making quick cash, you are not guaranteed to win and you also need 500+ to bet 100 each round. If you find a tournament that suits your combat style go for it. However there are other ways of making money. In one game I decide to play as a merchant, I accepted all the quests to collect taxes for lords, you can make like 6K from each. But when I collected the taxes I didn't bring them to the Lord strait away, I invested it buying goods and building factories usually the one that cost 10K. When I made enough profit I payed back the Lords.

You could do the same but invest in armor and weapons.

You will lose opinion with the towns and villages, -5 opinion, when you collect the taxes.

I never raid villages. The penalties to your honour, relationship with the village and relationship to the lord who owns the village mean its just not worth it. Whatever story line you imagine for your character, if you want to become an independent king at some point then you're going to need lots of honour and high relations with a lot of lords. That's tough if you've spent your time up till then raiding villages.

Yes tournaments are a good way to make money (and win renown and nice equipment) but for a brand new character tournaments are going to be pretty challenging. How you want to make money will ultimately depend on you character. There are quite a lot of threads out there about making money so you could google those for tips but I'll give my 2 cents below.

The first thing some people will do is sign up as a freelancer in a lord's army. You get a salary and a little experience and if there's a battle then you get extra experience and maybe some loot. Personally however I find its not worth it because you'll spend a long time sat in a castle/city or wandering around the map.

I prefer to strike out on my own, find a small group of looters, defeat them and then sell the loot and prisoners. Even as a new character on foot that should be possible with a small group of looters (3-4) straight away. With a horse you should be able to take on 10-15 and as a horse archer (my current character) I went out and slaughtered a group of 23 immediately.

Repeat the above, tackling gradually larger and tougher bandits and eventually deserters. Personally I like to do this on my own. As soon as you have companions or troops you get a lot less experience and loot. Once you've got a decent pile of cash you can start buying productive enterprises. These are better than buying land early on.

At this point you've also probably levelled up a few times so you might consider entering a tournament. The new style tournaments, such as those in Floris, aren't knock out and you can make a lot of money betting on yourself without actually winning the tournament. Its at this point that I usually do the merchant quest you get at the very beginning. Hire some peasants so you have 5 men, talk to the merchant and then disband them and tackle the kidnappers lair on your own. You'll get a lot of good loot.

Once I can reliably win tournaments I transition from bandit hunter to professional tourney fighter. Of course if I come across some juicy bandits on my way to the next tournament I'll take them. Likewise bandit lairs give a lot of loot and at this point you should be able to take most of them alone. I really enjoy the freedom of this phase, you can go where you want, lords won't be attacking you and you're capable of outrunning or outfighting pretty much all the bandits out there.

By now you should be level 20-30 which means you're not really a brand new character anymore. I haven't mentioned trade because I don't do it (I find it boring) but I hope that answers your question!

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.