There are several factors to consider when selecting paper for menus. If you are going to be changing it frequently or expect that customers will want to take a menu home with them, you will want to go with something inexpensive like 20# copy paper or a lightweight glossy paper. If you don't expect customers to take them, but still want to change them fairly frequently, then an inexpensive cardstock. It will be a little more durable than copy paper. However, these won't stand up to heavy use and will easily become creased, stained or encrusted with food.
If you don't plan on changing the menu frequently and don't expect people to take them, you can have your menus laminated or printed on a synthetic or poly stock. These will be able to be wiped down and some synthetics can even be machine washed. This is much more expensive to do, but they will last longer, resist staining and be more sanitary if properly washed. If you go this route, you might also consider having additional menus printed on an inexpensive stock for those customers who would like to take one home.
Paper will have to be replaced from time to time due to folds, stains etc. laminated will last much longer and unless you plan on changing the items frequently should hold up much better.
Should it be a laminated coupon bond or what? I want my menu to be creative and simple as well