Select by priority

I need some suggestions on how to construct a particular select that I
need. I have a table of addresses where the primary key is the
persons_id and a address_type field. The address_type field is a
character which specifies whether the address is for the home, work,
or mailing. A person can have multiple addresses though only one of a
type. What I want to do is select a list of address for each distinct
individual but wish to select based of priority that if the mailing
address exists, I get that one only. If there is no mailing address, I
want the home address and failing that, get the work address. Is it
within the realm of sql to be able to do that?

-- 
Prasanth Kumar
kumar1@home.com