emailing plugin that send emails based on database criteria

This is a bit difficult to explain. This is for a directory listing site.

I need an email plugin that will work in conjunction with the database (listings) to send emails based on the users sign up criteria?

HERE IS A SITE THAT IS DOING WHAT I WANT
https://estatesales.org/

In other words:
User indicates when they sign up: I want an email notification when new listings are posted that meet the following criteria:

5 miles from my town
antiques
vinyl records

This would be very much like a real estate site where user checks what they want in a house they’d purchase:

price range
4 bedroom
fireplace
pool
etc

HELP! ??
I have been going crazy trying to figure how to do this for my client!!!

thank you so much for taking the time to read this. ??