How do I back up to get my old apps and messeges back onto my new phone

Why? What happens when you try?

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Connect the old phone to iTunes. Make an encrypted backup (to have your settings and all private data there) and afterwards connect the new phone to iTunes (and don't set it up as a new phone, but choose iTunes restore).

If you are using the same apple id it should already be on that apple id. If you are not you cant back it up