Posting internationally from Australia to America

I sell on eBay in my home country of Australia. I'm looking to expand and to sell to the US market. I'm looking to sell parcels in sizes of 500g up to about 3kg. What is the best way to post these? I can send with Australia's main postage company, Australia post, just by Air Mail, this does not come with any form of tracking number though. How important is it to have a tracking number?

Or alternatively, should I look to send with one of the big international companies like DHL or EMS? My main worry is that shipping will be to expensive to compete with local sellers in America, who can charge much less for postage. All help is greatly appreciate, thank you.

I'm pretty sure they have international postage satchels (similar to regular pre-paid and express pre-paid) for up to 500g and also up to 3kg.