I started shortwave listening in the early 1960s with a Hallicrafters S120 (tubes -- I still have it), and moved on to transistorized models by Lafayette and Allied. Then, in relatively modern times, I got a digital Realistic DX-440 (Sangean 803A), which is about in your desired price range. Also, for power outage emergencies, I have a Grundig FR-200 (with a hand crank for recharging the battery).
The DX-440 does a decent job. I noticed from a net listing that Australia is listed on 9580 KHz at this time of day (between 8 and 9 am). I just checked that frequency, and was able to receive it on the U.S. east coast (with some static, but that's using only an indoor antenna).
For comparison, though, here's an example of what's available from Australia on the net (not counting tv) -- Australian Live Radio. I can understand having a shortwave radio for emergencies, or to receive special kinds of broadcasts, but for ordinary listening I think the internet is better.