Update. Can someone explain unraid and dockers? If this is a potential solution?
UnRaid is an operating system that was I guess originally intended to act as a NAS. However it is far more than that today. As you've probably seen it runs dockers quite easily. While entirely technically wrong, you can think of them conceptually as virtual machines dedicated to run a single application in a very resource efficient way - a bit like a virtual appliance. So instead of installing say Plex server software on Windows you run a Plex docker container which then is its own accessible Plex server. Via an app store called community applications, these dockers are very easy to spin up and configure. As a self confessed Windows person with little Linux knowledge, I found it all very easy by watching some videos on youtube by a guy called Spaceinvader One.
UnRaid doesn't use RAID but instead uses a method of parity that reserves your largest disk for parity as redundaNcy. So your total available disk space is Total disks - largest disk. This protects against failure of any one disk but is not a substitute for backups. You can also run no parity or dual parity if you wish as well as other things like cache disks and pools and something UnRaid calls Unassigned devices for disks outside the protected array but still shareable for specific purposes. Compared to other NAS/Server OSs it is comparatively slow in writing to disk (it has to write parity as well as the data each time) but fast enough reading so ideal in most home situations.
To answer the points in your original post:
Automatic client image backups to server (client or server triggered)
For Windows machines I can wholeheartedly recommend Veeam free. This doesn't use anything fancy on the server except a straightforward SMB share as the target. There are all sorts of docker containers for syncing and backing up if you want to explore other options.
Server that software applications can run, one drive, R etc
This is a little trickier. You need to see if there is a docker container for the application you want to run or a Linux equivalent. For example, depending on what you want to do with one drive, RClone might be a solution available on UnRaid. I use it with Google drive but it supports 30+ other cloud storage systems.
Media share that other machines can stream from
Bread and butter for all NAS really. Create an SMB share for your media if you want to keep it simple or introduce a media server like Plex, Emby or Jellyfin - these and more are available as docker containers in UnRaid's community applications app store.
WOL ideally (or at least scheduled up time)
WOL will be a feature of the motherboard you use rather than the software.
