Make readers to register to private website

Dear Bloggers,

I’ve got a website https://www.lucdp.com and my WordPress blog is on https://www.lucdp.com/blog

What I want to achieve is that the main page of my website is open to the public but I want the blog only to be accessible to registered users (And I will need to approve their registration).

I have tried multiple plug-ins but none of them does what I want to achieve
So here are the steps that need to be done:

-A new reader visits my webpage
-Clicks on blog and will see a “register” or “sig-in” screen
-When thet are new and register they will need to provide following details: First name, Surname, email address.
-I will then receive an automated email with their registration request
-I will then approve or cancel their application
-An automated email will then be sent to the new member including a login name and temporarily password
-The new member will then have to change the password and will then be able to login to the private blog
-Once they leave the blog they will sign out automatically

Members can only read the blog and leave comments, nothing more. It would be great to be able which members are online at the time.

Is there a plug-in out there that does exactly what I want? Preferrably free but I’m prepared to pay for it.

The plug-in needs to be simple as I am not a programmer and do not have any knowledge about php. But I can follow simple step-by-step instructions.

Kind regards,

Luc