My obligatory Python based answer.
Given the requirement not to use a data collection company (there are a lot of them out there) and that most if not all of the free SMS sending services are run by some of them you need something that can:
Check your emails
Run some filters on them (presumably you don't want spam notifications)
Send the SMS
I would ...
If you are not a FOSS-fanatic, i.e. if this is not a critical requirement, Google Voice will be just fine for you.
Just sign up for an account and it has all you need: you can pick up a US DID for free, it has built-in voicemail, and it can send recorded voicemails to email.
Voicemail greetings are customizable.