Great topic! Installing Postfix and running your own mail server is certainly an option, but I might recommend using an external SMTP provider. Back in the day you could just slap on postfix and start sending mail, standards were just a guide. Now sending email means following and keeping up with the latest standards. It means having nearly flawless headers, PTR, forward confirmed reverse DNS, SPF, DKIM for a little extra push, all that jazz.
I don't know about you, but when I think "make my monitoring system send me emails" I don't think "I'd like to get into the email business and become an expert in it." Yet, to run your own mail server, that is basically what you have to do to avoid very annoying issues like rate limiting, being filtered to the spam folder, or having your emails outright rejected by major email providers. If it sounds fun, by all means dig in, but I think you're going to be more satisfied with a simpler approach here.
For that reason, I'm going to suggest this tutorial which outlines a path for using an external email service (Gmail in this case) to send the alerts: