Whilst you can write to an NTFS partition from both Mac and Linux (with the correct free software), you are advised not to. Noone but MS and those who've seen the source code and APIs truly know how NTFS works, so as good as the open source implementation is, guesswork still exists within it. Sure, it'll probably work fine and you'll have no problems, but the potential exists for something to go horribly wrong.
You can read/write HFS+ on Windows using MacDrive, and there is a read/write driver available for Linux. That said, the same caveats apply as per NTFS.
FAT32 is tried and tested on all of them, so you need really to decide whether you're prepared to put up with a) file-size limits, or b) the possibility of problems arising from using reverse-engineered filesystem drivers.