My name is Michael. I've recently moved to Perth from the other side of Australia.
Check out realestate.com.au for rentals and properties to buy; it's a useful guide to prices and areas. I found the rental market harder to get into here than in eastern states. Real estate agents want you to play on their terms in the rental market. The sales market looks a little more open, but as a lot of people are moving into Perth, prices are relatively high.
Like most cities, the closer you live to the CBD, the more expensive housing is. In terms of geography, Perth is divided by the Swan river. North of the city is more established and includes the more expensive suburbs. South is newer and a bit cheaper. Avoid going too far east. The CBD is purely a business area with not much housing right in town.
The public transport system is clean, efficient and inexpensive. Trains and busses are well coordinated and the RFID tagging system used is convenient.
Hope that helps.
P.S. Look out for the drop-bears.