How to set up the following newsletter
Newsletter can do what you need. The description on the project page:

Multiple newsletters lists configurable on existing terms
Plain text or HTML out of the box.
Multiple schedules Each newsletter can have more than one schedule, e.g. Daily, Monthly, Weekly, manually or even custom, eg after 10 new posts for this term.
Centralized administration and configuration on a single page.
Users can customize the terms in the list they subscribe to.
Custom template per list.
Statistics (CTR and Open-Rate).
Drupal 7 only.

I'm using it on my site and it works like you've mentioned.