The easiest way is to set up a Yahoo group.
You can have the group name listed in the searchable index but only accept new members who submit their details to you first. Or you can keep the group completely hidden so that nobody will know about its existence unless you tell them.
You can determine the posting priorities so that either all members can post or just yourself. Members can choose to make their profiles available or to hide them. Messages can be read on the website or, if you've set it up that way, e-mailed to members. If you want, you can enable photo galleries so that members can post pictures and there are lots more options.
Take a look and see if this meets your requirements:
http://groups.yahoo.com/
Chris