For the weekly challenge, they could choose a certain objective, and choose either a campaign, Spartan Ops or multiplayer map.
For example:
They could make a survival challenge for one week, where they place you on a map in a certain vehicle (like a wraith) and you have to survive against waves of enemies, and the game would end when your vehicles explodes. The longer you last, the more XP you get. If you wanted to get a better time, you would only get XP past your original time.
And they could also do other challenges where you have to get a higher score, faster time or more kills, or anything else they would think of.
The top player(s) could get their gameplay featured at the end of the week to watch.