With your employment background, I’d go to Perth. Plenty of well-paid mining and mining-related work over there. Being a new migrant, they might ask that you travel interstate to mine sites (and I note that Western Australia’s a HUGE state), so if you do go there be prepared to be flexible. Lots of fly-in fly-out type jobs.
For white collar jobs however, Sydney and Melbourne (where I live) are your 2 best bets, being the larger and more commercially focused cities. Sydney is only slightly more expensive than the other capitals but really, not by much. You’d probably earn a little more there anyway. I certainly wouldn’t discount Sydney as a place to stay only because of cost of living concerns.
All major Australian cities (Sydney, Melbourne, Perth, Adelaide, Brisbane) rank pretty highly in liveability in pretty much any international ratings. Each have their pluses and minuses of course but you can’t really go very wrong with any of them. All have good places to live (check out realestate.com.au for places to rent).
Melbourne and Sydney are the most ‘vibrant’ in terms of culture, sport, things to see/do.
Western Australia and Queensland have the best weather and beaches. Sydney is decent too. Melbourne and Hobart have good beaches but unpredictable weather.
Hard to give you specific advice not knowing anything more about your preferences etc, but good luck!
Edit: BTW I’ve live and travelled extensively all over Aus (including all the cities I mentioned), so if you have further questions just ask.