> It needs to run on linux
That right there is going to imply some level of knowledge from the user. Expecting a zero-config install for Linux is pushing it to begin with.
> It needs to backup files in arbitrary locations, including spanning several partitions (one NTFS, one ext3)
And
> It needs good filtering / curation capabilities
And
> it needs to be easy to setup. I don't want to setup my own instance or mess with config files.
Are pretty much mutually exclusive. If you want it to be powerful you'll need to do the work to configure it. If you don't want to do the work it's not going to meet your needs, period. No product exists that will meet all of these criteria, even for Windows. I don't think a product exists that would meet half of them, and certainly if it does it's not open source.
What you really want is rsync over SSH to a ZFS volume with encryption enabled, or some other CoW filesystem that lets you do snapshots and access them online.
If you want to get close, go buy a Synology NAS and set up a nightly rsync cron to it, then set it up to archive to AWS Glacier. That'll get you most of the way to your ideal, and it'll be done instead of perfect.