Registering customers on wordpress sites

There are quite good number of Plugins. Go to plugins page to search as per your need.

https://www.ads-software.com/extend/plugins/

https://www.ads-software.com/extend/plugins/free-wp-membership/ is possibly an example of what you need.

Sorry, I’m being a bit dense here, but I want them to be able to register using their user name and own password, then be able to log in to see my posts on a particular page, not to access my admin side>

Is that what the above will do?

I do not know about any rock solid free option, but there are paid plugins like WPMU Membership Plugin :

https://premium.wpmudev.org/project/membership/

Or you can use Gravity Form with various addons :

https://www.gravityforms.com/