I'd like to display a simple password box where visitors need to enter a password before they can access the site.
Looks like a good option, I trust his plugins. There are a variety of other plugins available if you search for members, private, access, or a combination of those terms
I am a big fan of the Members plugin, but if all you want to do is have people log in to view the site, Registered Users Only is probably an easier option: http://wordpress.org/extend/plugins/registered-users-only/
This works pretty well also http://wordpress.org/extend/plugins/ultimate-coming-soon-page/ redirects non-logged in users to a custom message.