Subscriber button + post notification

Not sure if this belongs in everything else or perhaps installation.

Used to be a wordpress.com blog. Now a hosted ww.wp.xz.cn blog. Previously, we had “subscribers” and they would be notified when a new post was published, more as a reminder than anything else. My understanding is this was a feature built-in to wordpress.com sites, perhaps by jetpack integration?

Before moving we did take a download of that subscriber list. We’d like to add just a simple subscribe button for new visitors and then have automatic email notification of published posts and if possible import our existing list.

– can this be done without using the jetpack plugin (and wordpress.com), preferably simply?
– in looking around at various plugins (most seem overkill) it is not clear if the ‘subscribers’ or ‘members’ are kept in a seperate db or are created as new users with the subscriber role? Does it even matter for what we want to do?

And lastly, it needs to be free – hosting is already being picked up gratis by the two admins. We are not a commercial site and have no intentions of “paid” subscribers, marketing yadayda or anything like that.

I’m sure we’re not the only ones but my searches here all seem to turn up stuff related to jetpack.

Thanks