I have a lhassa apso/shih tzu mix. He doesn't shed, but requires frequent hair cuts. Mellow personality, no separation anxiety (I can leave him at home during the day). He wasn't down with being crate trained, but otherwise fine trainability.

Not very physically coordinated or athletic, but has plenty of energy for daily walks.

Adorable personality, gets along fine with other dogs and with children. Though he greatly prefers humans over dogs.

He does have some allergies that cause skin infections, so he's on a special diet. Lhassa apsos are supposedly prone to breathing problems because of their stubby noses, but I haven't encountered that yet.

Highly recommended breed. No more than 25 pounds.

Don't get set on looking for the "perfect" dog. All biological organisms have their limits and their own drawbacks and rewards. Sometimes you have to trade off one trait for another. Like some breeds are more prone to health problems, but they are generally more friendly or something. Also, you just don't know what things are going to happen in your dog's body or life. Generally with animals you never get what you were expecting, but you will end up loving them with more parts of yourself than you ever realized you could. Also, sometimes non-specific breeds, the mutts, are sometimes a better pick and can be fantastic dogs, but of course, you might not know beforehand what they will be like. I would also recommend a shelter dog, just because you can save an animal's life. But, don't be afraid to ask questions. Go up to the dogs and see which ones respond to you the best and which ones you respond to the best. Yes, look at the articles others have provided about picking a dog. Get one that will fit in with your lifestyle and living conditions the best. You know, go in with your heart and mind open and carefully consider everything, and know that some days you will get frustrated with your pet, just like you do with people, but the odds are that your pet will be the perfect pet for YOU, even if it isn't "perfect" according to various guidelines.

Also, a good way to keep your pet healthy is to take it to the vet regularly for checkups, give it some exercise and feed and water it right. Sprinkle that with lots of love and you will have fewer problems.

If non shedding is a big deal, go to you local shelter and look for something poodle-y. The rest is entirely dependent upon the individual dog--I've met hyper Chihuahuas that shredded apartments and retired greyhounds who spent their days couch-surfing.

Shelter staff are there to help match you to a dog, so go and ask questions.

And please don't buy from a breeder or pet store. Small dogs in particular are easy to breed on puppy mills, so much so that most pedigree/designer mutt small dogs out there are from mills.

Qlanders had some really good suggestions for me when I asked a similar question a while ago.
http://questionland.com/questions/9057-dogs-in-apartments

I think that an important factor is how much exercise the dog needs - Jack Russell Terriers are great dogs, for example, but are insane without huge amounts of exercise and interaction.

My roommate had a Papillon and it was a really neat dog. Super small and great for an apartment. They do tend to bark a lot if they are alone, especially at night. Miniature Yorkies are great too but expensive

Go for a mutt. Chihuahua mixes are generally abundant in shelters, and people I known who have them have had good luck with them. In general, mixed breeds have the best personalities and fewest health and emotional problems. Purebreds tend to be way more neurotic and high maintenance. If you do end up getting a purebred, I would say to avoid Jack Russel terriers; they are SUPER high energy, aggressive and territorial. Mini daschunds are sweet and smart but prone to congenital health issues (epilepsy, among other things). Of course, there will be unforeseen issues that come up, no matter how careful your initial choice of dog; prepare yourself with careful research and an emergency fund for veterinary care. Good luck in your search.

I don't have a breed recommendation, but I like the looks of this rescue http://www.gingerspetrescue.org/ Their adoption fees are steep but it's a great cause and they have lots of little mixed-breed dogs available.