Yorkies are the best! I may be a little biased though.
You can also get put on a waiting list at some shelters for certain dogs. That's how I got my boy Yorkie. Hubby put me on the list for a Yorkie and I waited a couple months or so and then got my little one - we got moved to the top of the list when my hubby DJ'ed a fundraising event for them. He was only about 4 when we got him and I adore him.
My parents just took in a cocker spaniel rescue after their Pom of 14 years died. The poor cocker spaniel was abused so badly they had to amputate a leg and he almost completely lost one of his eyes. Now she's just as sweet as can be and they love her. My parents are older (dad is 83) and they didn't want to take in a puppy because they didn't want to have to worry about what to do with the dog if they couldn't take care of it anymore so they didn't mind taking in an older dog.
Good luck on the dog hunt!