Well the costs can vary. Australia is in fact a good budget backpacker destination. More about that later.
Ok, flights vary in price. Probably the A380s are going to be more expensive. Other flights from the US all require a stop over, so you can shop around and find the best deal. Perhaps via singapore or even Korea (which seems to have a number of cheaper flights for some reason).
Anyway, if you are heading up to the barrier reef, you can actually fly to somewhere like cairns or townsville via singapore.
Really talk to a travel agent about this, as trying to get the best deals via online websites is not practical. But use both and compare.
The barrier reef is a little bit more complicated. You have a whole range of costs such as boat hire, scuba hire and so on. So it gets out of the budget range. You see the problem is that most of the reef is about 2 hours boat trip away from the coast. Worth seeing, as is that part of the world.
You can save money staying in backpacker hostels (basically you travel by bus, when the bus stops, people from the hostels line up to try and get you to get on their free bus to their hostel). You can also camp (in Aus