Of all the places that I would advise the OP to avoid, top on the list would be the popular destinations like Warsaw, Kraków and Wrocław, followed closely by Poznań and Gdańsk/Gdynia/Sopot. There are scads of wannabe "English teachers" scrambling for table scraps. The best jobs are already taken, and those require at least a CELTA, which is going to cost about $1000 US. In-company work and work during the summer goes preferentially to experienced established teachers. There's little for newbies. Few schools have any incentive to go through the harrowing process of getting a work permit, and most are reluctant to offer a real work contract, opting instead for useless "garbage" contracts (umowa zlecenie and umowa o dzieło), neither of which will help the OP land a residence permit. The few jobs to be had are mostly in lousy, low-paying schools like Berlitz, Callan, Avalon and "Direct Method" schools. It would take a lot of luck to land a real work contract in a good school for decent wages.
If there are still opportunities to be had, it is in the less popular cities like £ódź, Katowice and environs, Rzeszów, Lublin, Białystok and Bydgoszcz, or in smaller towns out in the province, particular out east, like £omża, Augustów or Tarnów, where the competition is far less intense. Furthermore, the cost of living is high in the popular cities, and the wages are not much higher than in the provinces, if at all. However, as the OP apparently has a particular destination in mind, this greatly diminishes his ability to cast his net wide and his chances of finding a suitable job in someplace far off the beaten path.
Sorry, but the boat has sailed for English teachers in Poland, especially for those who wish to work in the popular cities and who come from outside the EU. The OP is far better off remaining in Australia, where he can gain useful work experience and beef up his qualifications in order to increase his future earning potential, and perhaps earn enough to save up a significant amount of money, which will be impossible in Poland. Like I said, when you factor in the cost of airfare, the residence permit and the certification course, there's not much incentive to move from Australia to Poland.