Buying a house in South Australia

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We just arrived in South Australia as permanent residents. At the moment we are renting a house for $620 per week. We were thinking of buying a house. Would the mortgage payments for a house be much higher than the current rent that we are paying? If not, by all means, we would like to purchase a house. We don't want to live too far away from the CBD. The furthest we have considered is suburbs around Flinders University. We would be very happy to live in Colonel Light Gardens or any suburbs around there. We really like the idea of living close to the Marion Shopping Complex as we go there frequently for shopping and to watch movies. Also, the newly opened aquatic centre just makes it very desirable. From the north, we were thinking Prospect, Manningham or any suburbs around there. So realistically speaking, what kind of prices are we looking at? Would I be naive in thinking I could purchase a property for $500,000 - $600,000 around these areas in South Australia? We are looking for a house with 4 bedrooms and 2 bathrooms. In terms of financing, how do we go about arranging that? We don't work at the moment but we have income from overseas. Will this be a problem when trying to secure a home loan? What would be the downpayment for a house costing $600,000? What would be the weekly payments? I am just trying to figure out if we can afford it. Thanks.

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I forgot to mention that we receive $7000 every month from overseas. We have a family business back home and we can live comfortably in Australia even if we don't get jobs. Would this be sufficient proof of income or do we have to be employed in Australia to secure a home loan to purchase a house? The only other issue is, legally the business is under my parents' name although we get access to basically everything in the business including funds. Could this pose a problem? When choosing a location, safety is also a priority for us. We would like to live in a nice neighbourhood where kids can feel safe and there are no shady characters. I find that areas too close to the city like Mile End are full of shady characters.