Theming the default "node/add/content-type-name" content type form will allow you to achieve what you need as these forms are publicly available to users with permission. If the user has permission to create that content type, he will be able to access the page, so either create a link to the page (node/add/content-type-name) or use the default Navigation Menu link "Create Content" to take the user to the node/add page. Take a look at Theme a CCK Input Form for CCK2 & CCK3 to learn more about theming content type forms.
To remove the configuration fieldsets such as Menu Settings, Publishing Options, Revision Information, etc you really just need to change the permissions for the role. For example, remove "administer nodes", "administer menu", "administer comments", etc.