A good realtor will show you homes in the price range you ask to see. (Obviously, most owners who list a home at $60,000 will actually accept, say, $58,000. So it would make sense to show you homes priced just a few thousand more than the price you mention.)
If you would like to buy foreclosed homes, generally it's good to be able to pay with cash, because many of those homes will need repairs, and so will not qualify for a mortgage.
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