Let me say first, that it is impossible to absolutely predict how a puppy is going to turn out when it is grown and matured. The best you can do is to try to select the most alert and intelligent pup of parents that have the approximate size and color you desire.. Here are some criteria to go by that may help in the selection process.

Breeding - One of the first considerations should be the genetic make up of the litter. Are you familiar with the two families that are represented in the pedigree? Do they represent the  style that you are looking for? Looking at a  pedigree cannot tell you how it will grow up, but it can tell you how it should, if it is a true representative of its bloodline. That is all. However, that is something that is worth checking out.

Which sex to buy? - Most people prefer one sex over another for their own reasons, but  here are some basic pros and cons of each sex,... If not neutered at an early age, males may display aggressive behavior, wander more, and become jealous of other males. They could also become more "territory" oriented. Females are  in general more gentle, affectionate, protective. They do come in season (usually semi-annually) and attract unwanted attention from every male in the neighborhood .

Parents - Ideally you should see both of the puppies' parents. If the breeder does not own the male, find out why he (really) bred to that stud. Was it to sell puppies? (This is a judgment call.) Or was it because he admired the male? A good test of this is whether the breeder is going to keep any of the puppies. If you haven't before, try to see the parents (that are available)  This will tell you a lot. If that isn't possible, are there any older brothers or sisters (by a previous litter) that you could see?

Age of puppies - Puppies make the best adjustment to a new home when they are seven to nine weeks of age in my estimation.

Testing the puppies - There are no "fool proof" methods of testing for intelligence or temperament (aside from DNA that is compared to parents), but there are some simple tests that will help to screen the pups. Here are a few:....roll a ball toward the pup (or puppies). How do they react? Are they curious? Playful? Or do they avoid it? Drag an object on a string in front of the pup (or puppies). Again, what is their reaction? Some other tests are: shining a flashlight at the pup. Showing it a mirror.  Some hearing tests are: clap your hands. Blow a whistle. Make other sounds. Does the pup try to locate the source of the sound, or is it wary and hesitant?

How does the puppy react to being handled? - One recessive trait in shih tzu's is timidity or resistance to being touched and handled. I believe much of this is learned by the lack of being handled by the breeder,  sometimes it may be difficult to give pups individual attention, but it is vital. A pup can be born with the temperament that will tend towards shyness, but some pups get a little "careful" around humans from neglect. Also the competition in a large litter can cause a pup to become timid if it isn't born with an assertive temperament.

Body type and size - Size is very hard to predict. However, you can still sort out pups by body type. Are they fine boned (lean), or heavy boned (stocky)? Are they long bodied, or short coupled? Do they have big heads (in proportion to their bodies), or small? Do they have flat faces, or pointed noses( YUK!)? Take a critical look at each pup, and choose the one (within previous criteria) that comes closest to your ideal. Chances are they won't change a great deal as they mature.   Don't forget to check the bite, especially if you are considering a show career for your new puppy.  Some bites are so bad that digestion and health is affected; so don't neglect to look in the puppy's mouth.

Color and markings - This should be the very last consideration. This has nothing whatsoever to do with the temperment or health of your new best friend.

The only reason you should pay any attention to color is to see if the puppies are generally the representative color of the family or bloodline they come from. Some bloodlines are mostly parti-color, and some are predominately black, red, silver or gold. If the puppies are not the color of the family they are from, then something is not quite right. Check it out. However, if you are looking for a particular color, and won't settle for anything else, then beware. One color does not make a shih tzu any better than another!

Health - Finally, what are the conditions that the puppies have been reared in? Is it relatively clean, or nasty and smelly? The chance of latent disease or parasites goes up greatly in dirty conditions.

Have the puppies had vaccinations? Have they been dewormed? The owner of the litter should be able to supply you with the records of both. Without such care you are buying trouble.

Hopefully, these common sense suggestions will help you as you go to select a puppy. If the owner doesn't cooperate with a few simple tests on your part, then he may have something to hide.