I had a shitzu, the pronounciation of the name says it all. They are stubborn little dogs that are notoriously difficult to housebreak. I wouldn't take another one of those little fuckers if you gave it to me. The one I had was not unusual. It's a crap shoot with them. You can get a great one, or you can get a misserable little pissy shitter. You don't have to believe me:
http://www.yourpurebredpuppy.com/reviews/shihtzu.html
Frankly, take your lady to a pet store that has Lhasa Apso puppies. They look virtually identical to Shitzus, but are a slightly larger dog, more intelligent with a more stable overall temperment.
Either way, both breeds require
DAILY grooming. I cannot emphasize this enough. You also need to keep an eye on their ears, they're prone to getting gunky ears because they have floppy ears and sometimes a lot of hair grows in the canals.
As for the cats and dog house, either get young animals, raise them together, or get young adult cats that have dog experience from a shelter. If you bring a small dog into an established cat household the cats are going to exert dominance over them and fuck them up because no small dog can take a cat. You bring a kitten into an established dog house and the kitten is liable to be treated like a chew toy and develop fear of the dog.
Finally,
please, please, please do not declaw your cat, it's cruel and it risks ruining a cat's temperment or litter habits The absolute best scratching post is here and worth every dime (get the post BEFORE you get the cat, I totally recommend this, great company, great product, quick service):
http://www.topcatproducts.com/