For the most part I keep work and home separate, although there is some overlap as I exclusively work from home. I have several backup processes:
First, I take automatic daily differential backup images of the primary hard drive on my main desktop. (This is a Windows machine, so I use Macrium Reflect.) Images are great because if your drive dies or gets corrupted, you drop in a new one, copy the image over, and are back up and running as quickly as possible.
For the same reason I take images of the volumes on my home Linux server. For this I take an LVM snapshot, mount it, create a tarball, then unmount and remove the snapshot. These are only done monthly because the process isn't incremental or differential, so takes longer, and the contents don't change as often anyway. It could be completely automated, but I just have a script that I run manually, because I like to do any updates that have the potential to break things while the snapshots are open for ease of rollback. (I have a monthly calendar reminder to do this along with quickly checking that my various other backups are running properly, and backing up my phone using Helium.)
I continuously mirror the user folder from my desktop (and my wife's computer) to a Samba share on the home server using FreeFileSync. (There are many different ways to sync files, but since the desktops are on windows, this was easiest.) Then I run Crashplan on the home server to do incremental cloud backups of all these files, both to deal with the worst case scenario of the house burning down, as well as to catch any files changed intra-day, not caught by the daily disc images.
Misc: Regarding the phone backup, my preference is to do a full disc image, for the same reason as on the computers - break your phone and you can replace it and be back where you started in no time. Unfortunately that requires rooting, and in Samsung Hell rooting permanently devalues your phone due to Knox insanity. So for now I back up those apps that allow it with Helium, a couple of high priority ones using their built-in backups, and grumble about how I should just root. I also usually only bother to do this every few months, since anything really important on the phone is in the cloud anyway.
Except photos. I run FolderSync on the phone to continually sync any new photos to my OwnCloud on the home server via WebDAV (from which they're backed up to Crashplan), as well as back to Google via their photos backup tool, but in "standard" res - not as a backup, but just so I have my full photo library accessible on my phone.
I also occasionally fire up Thunderbird to download email from Gmail. I use the web client exclusively, but like to keep a local copy of all my email on the off chance I'm ever somehow locked out. It's highly unlikely, but the peace of mind costs all of 5 seconds every couple months.
I think that's it. Sounds like a lot, but I set it up incrementally over time, and for the most part it all just works. If I were setting things up fresh, I'd probably save some time by paying for more Google storage or something rather than using OwnCloud, and by using the CrashPlan family plan rather than syncing everything to the home server then backing up from there. Regardless, I do believe it's good practice to double-check whatever you use for your backups, at least every couple months.
(This is all leaving aside the Tempest servers, which use various RAID, master/slave SQL, LVM snapshot backups of the same sort I do locally, and rsync to off-site storage.)