rsync is used widely for mirroring servers... it's up to the task. If you want to be sure, why don't you do a few spot checks - change a file and see if it gets backed up.
Is it the best way? hmm, what are the requirements? If there are not a lot of changes, rsync is great. rsync is clever about sending only changes over the network - it won't send the whole file if only one part is changed. Efficient in network traffic, and supposedly at a small cost in CPU.
Sounds like you are running rsync from a cron job? Look at the rsync command in crontab (man 5 crontab) -- if you redirect the command output to /dev/null you won't get the email. Sometimes you need the email to troubleshoot though, so YMMV.