New smartphone and transferring stuff to it

After more than four years of service, my Android phone (Motorola Droid Razr Maxx) is on its last legs. I bought it largely for its great battery life and it did not disappoint, but it has gotten very slow and the battery is finally showing signs of age. I'm going to replace it with a new Motorola Z Play, which is relatively inexpensive for a phone and also has a great battery.

The people at Verizon say they can transfer contacts and photos from the old phone to the new one. What about other things, like text messages and the sound file for my ringtone? Does anyone know of a reliable way to transfer them? I've poked around online but haven't come up with anything.

Thanks in advance!