You must be able to distinguish between a stable and unstable grave marker before you attempt to make a rubbing or even to gently clean away debris. When in doubt, don't. And it's best to get permission before doing a rubbing. In some states, such as Massachusetts, it's illegal. As with historical documents, tombstones are artifacts that must be treated with respect and care.
Many people use large sheets of butcher paper to make rubbings.
If you're traveling, paper is harder to manage, and it tears and creases. Interfacing can be folded in your suitcase, it doesn't tear, and you can iron it when you get home. Buy interfacing in bulk, about 10 yards at a time, to keep in your cemetery tote bag. If you take anyone with you to the cemetery, especially kids, they'll want to try making a rubbing, too, because it's so much fun. But please make sure they don't get any crayon or wax on the tombstone.