Backing up to the computer and then restoring to the new phone is probably the quickest way to do it.
The other way of course is making a iCloud backup from your old phone then choosing "Restore from iCloud" when booting up your new phone. Be sure the old iPhone no longer connects to the internet (Airplane mode) after you make the backup. Also, before restoring to your new phone, be sure to disable "Find my iPhone" on your old phone.
If you backup/restore from your computer, before starting make sure that all of the apps in iTunes have the latest versions. If you don't do that, you will be restoring old versions of apps to your new iPhone.