How to transfer iphone to new iphone?

So I have the old Iphone 4(Verizon) but I just bought a used 4S off a friend of mine. I tried to switch my phone number and stuff to the 4S but on the Verizon site it says "The device you're activating is not compatible with your current plan. Please select a Data Plan below.".

Now I'm grand fathered in with having unlimited data. But I thought if I bought a new iphone outright that I'm able to switch it and still have unlimited data.

Follow This! Settings> iCloud> Then back up your device using your iCloud account, Get you new iPhone and do the same thing but click on the thing that says something different right where back up used to be.

You can transfer contacts from iPhone to iPhone using iTunes, iCloud or iPhone data transfer software.