By default (and from what I've looked at thus far),
at dumps the standard terminal text output to
echo "hello" | at now + 1 minute will save a log about the command) Is there some way to disable this, or an argument I can pass in to keep it from happening?
Redirect your output to null
echo "/path/myscript > /dev/null 2>&1" | at now
at doesn't dump it to /var/mail/username, it emails it to the user. If your local mail server is configured to store messages in /var/mail/username, then it delivers them there. If you don't want them there, then configure your mail server differently.