For a simple, outgoing only email service, ssmtp is probably the easiest to setup. This can send email through your institutions smtp relay, or if you’re in a pinch, gmail can be used. In the later case, it is necessary to use an existing gmail account to authenticate. If setting up several machines, the same account can be used, but there are benefits to creating a separate gmail account for each machine - primarily to make it a bit simpler to identify where the mail comes from.
sudo apt-get install ssmtp
Then edit /etc/ssmtp/ssmtp.conf something like:
root=GMAIL_ACCOUNT@gmail.com
mailhub=smtp.gmail.com:587
rewriteDomain=
hostname=GMAIL_ACCOUNT@gmail.com
FromLineOverride=YES
UseSTARTTLS=YES
AuthUser=GMAIL_ACCOUNT
AuthPass=GMAIL_PASSWORD
The downside is that all emails will come from the same account (GMAIL_ACCOUNT@gmail.com).