Frankly, I'm not at all sure the cheapest place will be Australia. I'd check out New Zealand & Thailand for starters. And possibly the US
The cheaper options are more likely to be away from the major cities, although your cheapest accommodation option is probably to rent a room in a house which may be a bit easier in the city.
The cheapest way to do the flying is to study way ahead of the flying lessons. Do all the theory first. Memorise all the checklists & practice with a picture of the instrument panel. Understand the flying syllabus and prepare for each lesson. Know what you are setting out to learn before you get in the aeroplane. Probably do some simulator work too (PC at home with X-Plane), it helps get you into the routine. This will be the difference between doing the flying in close to the minimum hours vs way above the minimum hours.
If you are coming to Australia, I'd be choosing a flying school that you like and can hang around in between lessons. Maybe do odd jobs to reduce flying cost. Maybe take a job with a maintenance hangar sweeping floors so you get to see aeroplanes in pieces and see how they work. Take any rides you can with other guys. Quiz the instructors on the ground. Listen to radio calls and rehearse them on the ground.
Choose your instructors. The instructor you learn best from is the one you like best. Preferably one that is experienced and confident in how to instruct.