Limit users to posting on one page

I would like to limit users to posting on just one page.

This is a confusing statement, so please rephrase.

But I don’t want to force everyone to log in just to view my website.

User’s don’t need to login to view your site–it that is happening then you’ve got a plugin doing that.

I want to limit the ability of authors or contributors to posting to just one page.

You don’t post to Pages, but you can ‘attach’ categories to posts (not Pages) so look at http://wordpress.org/extend/plugins/capa/

generic:
* http://wordpress.org/extend/plugins/tags/restriction
* http://wordpress.org/extend/plugins/tags/restrict
* http://wordpress.org/extend/plugins/tags/members
* http://wordpress.org/extend/plugins/tags/membership
* http://wordpress.org/extend/plugins/tags/register
* http://wordpress.org/extend/plugins/tags/registration

Think it’s what he meant, yes.