As with Anne above, we have cable. We have excellent speed (13.6 mbps) and never a problem. We have pretty close to the fastest cable connection you can get in Adelaide. Many people within metro Adelaide have reasonable connection, but there are some black spots.
Like you, a major consideration for us is internet connection, which we use for working from home and is a priority when looking at houses. The NBN map is a bit misleading, as it only covers the 'new' NBN, which was going to cover pretty well everywhere in Oz - but no more sadly. There are other ways of getting fast connection, such as ADSL2 and cable.
We have never had an issue with being able to be connected in 3 different houses. We have always been with Telstra. However, if you type our current address into the Telstra website, it says 'Sorry, Broadband is not available in your area' - which is rubbish. So you do need to contact them, not rely on the website.
Sometimes it is a matter of you get what you pay for.