Q:

Linux filesystems recoverability

I am on Debian 8.6 and have 1x 4 member RAID6 2TB size in effect.  Apart from backup system I now need to decide what filesystem to use.  
The purpose of this array is reliability, availability, and the possibility to recover deleted files. 

A:

Use ext4. 
The mature (and not stale) choices are basically ext4 and xfs.   Redhat like XFS for it's scalability, performance.   I have nothing against it but ext4 is more commonly used and hence slightly better understood (community documentation like StackExchange). 
Don't expect to recover unlinked files. 

There used to be an undeleter for linux ext2.   There isn't one that works for modern filesystems, in my experience. 
(When the FAT filesystem on your camera breaks with much-wanted photos on it - or you accidentally delete all - photorec is amazing.   It works for many document types, not just photos.   But you don't want to run it the server of a small business, it can't exclude files which are not deleted and it can't tell the filename). 

New-fangled copy-on-write filesystems can carry historical snapshots, allowing recovery if you delete a file that existed in the last snapshot.   But:
btrfs is not considered stable in Debian.   (Everyone tells you to use the latest upstream kernel for btrfs, or possibly a distribution like SUSE where they were backporting fixes).   btrfs' nascent native raid5/6 code was recently discovered to be broken and AFAIK still needs rewriting. 
ZFS would be a valid solution.   But since you don't mention it yourself, I would not suggest it.   It is not even included in Debian.   ZFS is kind of its own thing... it even has it's own weird cache system separate from the normal Linux VFS.