Moving to a new Windows smartphone maintaining the same settings/configurations/files you have in your “old” phone, is now very easy and only few steps are needed even though your old phone is not a Windows smartphone (only a Bluetooth connection capability is required):

1. Use the Transfer my data app that allows to copy your contacts from an old phone (even an Android or iOS one) to your new Windows 10 mobile / Windows Phone via bluetooth. Your old phone may also be capable of transferring text messages and pictures.
   

   Transfer my data via Bluetooth

2. If your “old” phone was already a Windows one, force its Backup (Windows Phone 8: Settings -> System -> Backup – App list + settings – Backup now button ; Windows 10 Mobile: Settings -> Update & security – Backup – Other options – Backup now button) in order to have updated the backup you have in the cloud. Obviously you should have already left checked all the default backup options related to the Start screen layout , accounts and others. You may want also to backup the SMS going to Settings -> System -> Messages – Backup SMS). See also Backup my stuff. During the setup of the new Windows 10 mobile smartphone you will be requested if you want to recover one of the backups your user have on the cloud: if you choose the last one just done, the same configuration (even the same Start page setting) will be recovered and you will only need to possibly re-enter some passwords for some email  accounts (at least the ones that requires a 3rd party authorization like Gmail).
3. Possibly use the Windows Device Recovery Tool (download) to update both the S.O. and the firmware at the latest release and possibly to fix software problems on your phone (be careful that this tool may reset your phone): it works on Lumia, LG, HTC One, and HTC 8X phones running Windows Phone 8 or later versions. For non-Lumia Nokia phones, use the Nokia Software Recovery Tool instead.