This is a little more complicated than everyone is letting on, but you can do it.
Here's what I would recommend. The free version of Helium only backs up to a folder inside the phone and you don't need root, but in order for this to work you have to also install the desktop version of the app to your PC. You connect the phone to your PC and then fire up and sync both apps on phone and PC. This puts the phone in a special mode I guess and it backsup everything to a Helium folder on your phone whatever you select to back up - just back up application data only. When you are done, close out of Helium and while the PC is still connected to your phone (via USB), using Windows file exporer copy the Helium directory from your phone to your PC.
Next, use Smart Switch on your new phone for all the standard stuff, i.e.: Pictures, Contacts, Apps, texts, etc. Next after you've got all the stuff on your new phone via Smart Switch, plug phone into PC and copy the backup from Helium folder you saved on PC to the same folder on your phone. Fire up Helium app on your phone and select to restore your app data.
Done. All your apps you use on your new phone will now look just like they did when they were on your old phone with all the data.