The biggest determent to doing origami, other than time and complexity when you get to harder pieces, is quite simply the origami paper. It doesn't cost much, but like any type of crafting it does require some monetary devotion.
Get the origami paper question out of the way by using what you have lying around - namely, money. Check out this video to learn how to fold an origami Statue of Liberty from dollar bills.
This origami Statue of Liberty is folded of 4 dollar bills. (No glue is used).