Qantas has never lost a jet aircraft to a crash a feat no other airline in the world can boast
Now let me see, Virgin Blue? Nope never lost a jet aircraft either, I suspect there are many, many others...
In answer to the question, get a licence, get some experience, apply to the majors, it's quite simple really. Pretty much any licence will do, but I notice the companies on your list are all US based, so then an FAA licence maybe better! Of course to work in the US you need a 'green card' if you haven't got one of those then I would be targeting countries where you do have 'right of abode'.
An Australian licence is accepted in most countries except Europe and the training in this country is a fairly high standard. If Europe is your goal then only a JAA licence will do.