These days I usually start a new song in Ableton Live. With Fade Files we use Reason almost exclusively, with the exception of our early tracks, which were done in Pro Tools. On recent writing sessions in London we used either Logic or Pro Tools. There are other options still. I guess the main thing for writers is to know one software really well and know your way around Pro Tools and possibly Logic.
When I need to send files off to my co-writers I just need to make sure they will be able to open them in their preferred software. The easiest way to do this is to create (or “bounce”) an audio file for each track, or sometimes group of tracks. And vice versa. I get their files back, and so on.