If your organisation was such that you required an MTA then I would suggest that you probably wouldn't be asking what the "best mail server for Moodle" is in this forum. You'd have been hired due to your mail administration skills.
"... but only as a session cache and not as a session handler"
I'm not sure I understand what you mean. If you set up Redis sessions then the sessions are stored in the database. As opposed to the moodledata area. What else are you expecting?