Is there a way to produce automated welcome emails for individuals who sign up to receive our newsletter?
As @ericG suggested the CiviRules extension can do this. You can find the CiviRules extension here: https://civicrm.org/extensions/civirules and documentation on the extension is here: https://docs.civicrm.org/civirules/en/latest/.

If you want to send an email you will also need the Email API extension: https://civicrm.org/extensions/e-mail-api