You see those choices because the iPhone(s) has/have not seen this computer before. You may choose set up as new, as that will not destroy any information on the iPhone(s).
But be very careful. Each of your children should have her/his own Apple ID, regardless of their age.
Help your child set up an iPhone, iPad, or iPod touch - Apple Support
And once each child has her/his own Apple ID, their iPhone should be thoroughly cleansed, so only her/his own information is on the iPhone.
What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support
If appropriate and if you wish, you may set up Family Sharing.
Family Sharing and Apple ID for your child - Apple Support
But when backing up each iPhone to iTunes, each Apple ID should be backed up using iTunes in a different user account on the Mac.
Apple Menu > System Preferences > Users & Groups