Fly into cairns work along gold coast to sydney then to melbourne from there
Budget: Australia is expensive. Not as expensive as Norway, but about as expensive as Japan. I wouldn't recommend hitch-hiking (it's not impossible but not very common either). Enjoy the beaches, but either do you research unless you want to only find the crowded tourist-trap beaches or go during the weekdays when they're much less busy (unless it's a particularly hot day, then it will always be busy).