In a former life as an Email server admin for multiple entities, all I can say is 'Wow!'
What's the purpose of email coming from a moodle server?
There are forums ... we are participating in one discussion here, are we not? Did you ever look at the header of a message coming from these forums?
Your message to the forum delivered to the address am using to get mail from this forum has this:
"Pablo Britos (via Moodle.org)" <firstname.lastname@example.org>
I can't directly communicate with you ... heck, you might not want me to!
As a teacher, I might want to get notifications of assignment submissions ... am not going to reply to those messages, am I?
Or, notifications of students who are in danger of dropping out of the class ... they aren't accessing/interacting/completing assignments, etc.
As the moodle server admin, do you get those 'nags' from your server? Informing you that your version of Moodle is behind and the 'strong suggestion' that you keep up to date?
The noreply address ... if one attempts to use gmail.com (some folks thing Google collects too much info - and they do collect), hotmail.com, or yahoo.com users systems and whatever their mail protections are will probably tag that as spam ... not coming from the true server from which the message generated ... and not even deliver it to the spam folder ... but drop it on the floor - meaning it is obliterated, address is blocked from that time forward ... even if the intent was legit.
On your Moodle server, are you running a full blown mail server ... that can send as well as receive?
Does your moodle servers fully qualified domain name have in DNS the following records: MX, SPF, DKIM.
If you do setup a noreply inbox and your mail server doesn't have caps ... how large an inbox can get before it rejects any new messages, you could fill up all available free space on the device. And if you have an all in one Moodle server - web for moodle, db for any applications ... your DB's will suffer - get corrupt - maybe even to the point of no recovery.
That noreply address has to be checked ... by a human? Guess one could figure out a way to empty the inbox if it got too large, but then what was the point?
So ... my 2 cents: the noreply address goes to a non-existent user (noreply) @yourfullyqualifeddomainname of the moodle server. That mail *never leaves* your server.
If you have a ton of outgoing mail, do use an SMTP relay.
Believe me when I say, you don't want to run a full blown mail server ... period. That 'hat' and that 'hat' alone is a full time job ... time better spent developing content for the Moodle and interacting with students/particiants, me thinks.
Uhhh ... there is no 'best way' ... depends upon too many factors that one cannot really control beyond your Moodle server.
My 2 cents, of course ... you are certainly free to try/setup whatever you like! One last piece of advice, whatever you setup, take notes, so if you discover a 'catch 22' - undesirable unintended consquence, you can reverse what you did and try something else!