Changing my iPhone, need to completely back up my phone, how?

I'm changing my phone provider. I'll be going from Sprint to T-Mobile, I have a iPhone 4S and going to the iPhone 5S. How do I completely back up my info. Like contacts, photos, notes, etc.

1. Connect your iPhone to your computer
2. Sync with iTunes (to make sure all songs etc. Are on iTunes)
3. Go to iTunes > iPhone > Back up on this computer

It best to do it through iCloud.
Go to settings
Then iCloud
Scroll to the button
Click storage and back up
Turn on back up then allow it to back it up.
This may take a while but it saves all apps and pictures etc. (except music) you can still use the phone while it's backing up.
When you get your new phone it'll have everything your old phone had