I'm going to start a website where I need a Signup and Sign in system. And when the user is signed in the user will get access to stuff that only members can see an access. Would HTML be the best way to go then?
As John said before me, HTML isn't the right way to do that...
but... just for be more clear...
there's the "protection folder via .htaccess".
I think that each website administration panel let you to create "protected folders", those folders accept a list of user-password combination that you have to build up by your side.
of course, this is NOT automatic.
For automation you have to learn/use Server-Side languages as suggested: Php, Asp, Jsp... choose the one that catch your attention...
The previous answers are correct, but assume you want to build the server-side stuff yourself.
If you're interested just in "setting things up" you may want to look into Web Hosting companies that offer a "Content Management System", which probably suits your needs. A decent list of systems can be found here:
One of the more popular systems is Drupal I believe, for which Stack Exchange has its own Q&A site: