We are not talking about a disk that will contain a operating system, right?
To organize the files there is something called directories (aka folders), which do not bring any partitioning issue. File searches can be restricted to a directory.
One directory can be for the backups, e.g., with Trisquel's "Backups" tool in the "System Settings". However the backups may end up occupying the whole disk. "Backups" does that (and automatically removes the older versions of the files when there is a shortage of space). That said, since it backups in an incremental way, it may take quite some time to fill up the whole disk. Well, it depends on how much data you back up and how often those files are modified...
Anyway, backups may end up filling the whole partition (it is "normal"), it makes sense to have a separate (and large enough) partition for files you want to carry, besides the partition (the rest of the disk) for the backups. And I am talking of backing up files from another disk (and the external can be backup on the other disk: "cross backups"). Indeed, although you can backup on the same disk, it is not particularly safe: the disk (the hardware) can fail, suffer from an accident (it falls), it can be stolen, etc. In such eventualities, the data on all partitions are lost at once.
Modern filesystems do not suffer from fragmentation problems until they are almost full. You can choose any filesystem and they will be readable from any operating system with a kernel that supports the type of the filesystems. XFS is often said to more efficiently deal with large files (megabytes already is considered large). However XFS cannot be shrunk. That would be a problem is you choose to have several partitions but oversize a partition with an XFS filesystem and need more space for another partition. Btrfs is efficient but it still is rather new: the probability to lose data, although very small, is higher than with a more mature filesystem type such as ext4. That said, it is users people do not adopt Btrfs that it keeps on suffering from this novelty issue (it actually is not that new anymore).
So, if I were you, I think I would go with two partitions: one for files to carry (I do not know how much you want to carry but you had better over-dimension than under-dimension that partition) and the other partition (the rest of the disk) dedicated to the backups. Both can be formated in ext4 but you may prefer NTFS for the first partition (so that you can share files with Windows users).
