Yes, am 'ancient'. :|
When you look around for SMTP services ... first check with where you are hosting. Many offer a setup where by customer has 10,000 free and then X$ amount over.
Dunno what your volume of outgoing mail would be and not sure there is any tool that moodle admin has that would tell you that.
I, personally, use SendGrid's API. But my sites are sandboxes and very little mail come from them.
Do learn the gmail show original thang so you can tell students how 2 ... just in case.