Storage disk format to use to be utilised by all OS

Generally I would now recommend to use exFAT; it's supported on the three major OSes and supports large files and a large number of files.

But if you want to use NTFS, you don't have to buy anything.* See How to copy files to read-only NTFS hard drive on a Mac – there are non-commercial programs to write NTFS on Macs. Just install ntfs-3g via Homebrew and follow the instructions that you're given on the command line. You'll also need osxfuse.

Then, you can use NTFS without problems, and also don't run into an issue with large files. With ntfs-3g, NTFS volumes will be mounted with read/write support, and in practice I've never experienced problems with it.

_{* There are commercial variants that promise better speed and support, like Tuxera and Paragon, but they are not strictly required.}

If I had to do something like that I will go for a spereate NAS drive. You can setup up FreeNAS. This has the ability that you can write from different OS'es to one storage. You may need a seperate machine for this, apart from the one with the 3 OS'es on.