The secure approach would be to make a copy of the drive on another drive, using the dd command or any cloning software (like "clonezilla"), and try recovery attempts on that copy. So, you can repeat recovery operations using same or other software.
You have to avoid using the drive for other purposes during recovery work. Of course, don't boot from this drive, don't install any other software there. Don't put recovered files in the same drive (use any other drive, network drive, usb drive or memory).
Concerning software: I know some m$windows (non free) programs that could work for fat/fat32 and ntfs filesystems. I remember now "Easy Recovery" and R-Studio (2 versions, for fat and for ntfs). I used them in the past with moderate to low success, among others because I couldn't keep the system out of work for a few days (it wasn't mine). But in that case the partition and filesystem remained the same (files were deleted and trash folder purged).
In your case, I think you can try the (free) programs "TestDisk" and "Photorec", both on a same live cd.
TestDisk is a partition recovery software that scans the disk to find possible partition entries. Photorec scans the disk for specific types of files (originally developed for photo file recovery but extended to many other files too).