rooting a phone usually wipe it entirely !
if you want to backup a phone you already used, recommending rooting is maybe not advised as he will lose everything and will have nothing to backup anymore.
of course, then he can make full rom and user data backup, but I suppose he wants only backing up his data.
some manufacturer might have tools to backup (sms, contact list, photo, etc.) to computer. if not enough, you'll have to use a program but most will need root to backup also your settings and savegames for example.
you can also use adb command line interface (it's an android developer tool) on your computer, but you have to learn how it works and which command to type to do backups of everything, or single app, etc. adb might not backup everything as some programs are protected.
there are GUI or layer to use with adb, like titanium backup.
I never use it, but based on all the reading I did, I'd recommend Titanium. It's using adb to do the backup without root.
you can also make a backup, root (will wipe your phone !!), and restore backup to get them back on your now rooted device. if you don't do that you'll lose everything when rooting it.
https://www.titaniumtrack.com/lates...supports-backups-from-non-rooted-devices.html