Challenge mode:
First, find a friend who often plays at the same time you do. Next, each of you needs to make a new account (don't pay another $5 if you're a member - keep this account F2P). Then you must decide on a world which you will both join. In order to stick to challenge mode, the following five rules must be followed at all times on these accounts:
1) You must always play on this world, no exceptions
2) You cannot access any in-game stores (NPC shops)
3) You cannot use the Grand Exchange for anything
4) You can only trade with the aforementioned friend
5) You cannot complete any quests except the tutorial
Basically, you and your friend need to / should work together as much as possible, because the only way you're going to get items is through monster drops or creating them yourselves. Archers would be pretty much impossible to play since you cannot create arrows, but if you get them from drops, then it would allow you to train ranged.
It'd probably be best to assign roles, too. One of you can become good at mining and smithing to create armor sets, while the other fishes and cooks food to use while training. Since cooking doesn't take long, that person could also work on Runecrafting. Magic would be limited though, since you could only get runes like Laws from drops.