A desktop or server computer can be backed up, in whole or part, with only 3 components: the computer, backup software, and a connected storage device.
How do I accomplish the same for an Android device?
All of the answers and discussions I've come across so far rely on having a PC or a cloud service or both present.
A complete answer collection would include bare metal backup and restore, but for the moment I'm most interested in backup of user data, that is everything added and configured after one logs in to new device for the first time. Apps installed, docs and settings for those apps; wallpaper, icon and launcher layout, and so on.
There should be at least some ability to pick and choose what to restore from the backup archive.
I'm on Lollipop 5.1, but please don't feel need to restrict to that version unless necessary. I am partial to using sdcard as backup storage destination, while being open to other possibilities such as a USB device or LAN share.