Veracrypt lets you create encrypted partitions (or encrypt them in-place).
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I think this is the way without overspending on expensive hardware crypt drives.
I don't know how well the equivalent Linux tools work, but when I tried repairing damaged filesystems in Windows with chkdsk, I had more success with NTFS.
Or alternatives which lives in both worlds?
Using a harddrive enclosure that handles the encryption would probably be a very fancy (and expensive) alternative. The IODD 2541 comes to mind, but apparently there's a successor out now with the IODD ST400 (which requires a 7mm thick 2.5inch drive instead of 9.5mm). This video goes into some detail what it can and can't do. Apparently the software for managing VHDs is only for Windows and requires a hard disk with NTFS, but the file system on the VHD itself can be whatever you want. So this still doesn't solve the main question of which file system to choose.. and I can't really give any advice there either.