To password protect more than a single page, such as a Members Only Section or select pages for a group such as members, officers, leadership, etc. we typically use the Membership Pro 2 plugin from WPMUdev.
This can be installed on a per-site basis with the normal plugins menu. Information on setting up can be found here
Add-Ons are available to password protect posts by category, URL structure, etc.
To HIDE the “REGISTER” link on the Login box add this snippet of code to the custom CSS of the theme/site.
.ms-membership-form-wrapper a {display:none}