We need a low entry barrier and no matter how small a full project is, it is going to imply a significant amount of work and trust in order to work out. Prospective product managers could be directed to Bugzilla, where we have thousands of enhancement requests waiting for someone to take action on them (and not only enhancement requests: product managers also need to have a sense about current issues and how to prioritize them). We also have pretty decent documentation about Bug management that is mostly useful for someone going through enhancement requests.
Once someone has done some exercise in our Bugzilla then everybody will have a better grasp of the tasks to do next. Also getting CCed in 40 reports you just shuffled is a good way to meet people and stick around...