how and what to add to WP site to have a mailing list?

In your case I’d start off looking at an outside email system that is custom-built to send out newsletters. My personal favourite is MailChimp, but there’s a lot more out there, so have a look and see what can suit you.

When you get that figured out you can see what sort of integration is available. I know that there’s a few different forms out there that work with MailChimp and other systems for sign ups, etc, so there’s lots that can be done.