Restoring options iPhone 4S

Contacts are designed to be synced to a supported application on the computer or a cloud service.  If you use the device as designed, they can simply be synced back to any device at any time, no restore needed.

If you choose to not use the device as designed and instead rely solely on the device and it's backup in iTunes, then a restore is required, it should include contacts, and the restore is all or nothing.

When restoring you have the option of "as new" or "from backup".  You select an option and iTunes restores the device.

If you've never backed up the device, then there is nothing to restore, the only restore option will be "as new".