Those are some quite interesting ideas. Although I remember seeing that idiotic movie called "A Knight's Tale", and seeing quite a few choices of competition. I think that would be fabulous. Just imagine this:
You walk up to the Zendar arena master. You greet him, and then he asks you what tournament you want to compete in; and a list comes up on the bottom screen with selections like jousts, arena melee, target archery, spear/knife/axe throwing, heck, maybe even a horse race.
You'd pick one, let's say target archery, and he says to gather up your bow and come back to him when you are ready. The cost for entry into the contest should be about forty or fifty denars (Most who enter the contest will probably have been playing for a while, for archery requires many skills to be mastered) When you return, ready for the competition, he'll wish you luck and you will be teleported to a long and thin range, with painted targets at different distances from you. Your arrows will be practice arrows from the arena. Maybe some stands, with a minute audience. Other archers stand to the side, and your are told to fire a shot at the first target. Your accuracy will be displayed, and will determine whether the audience boos or cheers. This continues until the last target at the far end of the range, and you will be scored. If you get first place, then you receive either a light sum of Denars, or some archery-related item such as an expensive bow, or an amount of high-quality arrows. The throwing contest would not differ greatly, but the reward would probably always just consist of gold.
Or maybe you'd pick the arena melee. Entry cost would probably be no more than ten denars, as this would probably be the contest the beginners would join in. You would be fitted into a standard suit of cheap plate armor which your opponents will share. Your weapon will always be a two-handed practice sword, and like the armor, your enemy will have the same weapon as you. You would be fitted in a small, square pit with walls of stone and would be surrounded overhead by spectators. The pit would be about 15x15'. Quite simple; whoever is KO'd first is the loser, and the other is granted a modest reward, like an amount of gold or an average blade.
And finally, the joust. This would be the most popular tournament, and the largest audience would appear here. To enter you would need nearly one hundred denars, and be quite well equipped. You would need a horse, suitable armor, and of course a lance or two. You will run four or five times, and if you can best each of your opponents you will receive a hefty sum of gold and/or a valuable miscellaneous item. The reward would vary depending on your skill, popularity, and that of your opponents.
And that brings me to popularity. In Gladiator mod, each time you win a battle, your popularity with both the people and the nobles increases. There could be a system similar to this. The more popular you are with the people, there will be larger crowds and more motivation, and your opponent will be booed more and their morale will be a great deal lower, which COULD (I'll mention this in another thread) alter their performance in combat... With the nobles, you could be granted higher positions in armies, maybe greater rewards, important quests, etc...