Aside from paper, in which the weight varies per project, here are some tools that you may need to get started with papercutting. You can just begin with the basics: a precision knife, cutting mat, and pencil for illustrating those awesome designs! (:
A friendly note:
When you make a purchase by clicking through the items in this list, I do a happy banana dance somewhere and get a small commission. (: I just recommend products that I truly like and I hope they will be excellent for you too!