If you plan ahead you can use leaves- just save them in the fall.
Paper works well, but if its too wet, consider leaving the top off if it's a dry day, to allow for more evaporation.
I've been composting a long time. My bin used to be under a huge tree that was always delivering leaves directly into the compost. I didn't appreciate that until I moved, now I have to collect and save leaves, shred kids school papers, etc!