Chinchillas as with people vary greatly in personality & appearance. So how do you find the one that's right for you? What you're looking for in a chinchilla will vary greatly in what you want the chinchilla for. I have broken it down into 'pet' and 'breeder' categories.

Pet
When looking for a chinchilla for a pet the 2 most important things to you are probably going to be health and personality. Best options are buying from a small hobby breeder or adopting. With adopting comes the risk of unknown genetic background, but most rescues will have done a complete vet check on the animal. Rescuing is also extremely gratifying and it's comforting to know you gave an animal in need a great home. When buying from a breeder for a pet animal I would go with the smaller hobby breeder as opposed to the larger breeder or rancher. While both will produce quality animals, more often then not the hobby breeders' kits will be better socialized, as they simply have more time to spend with them. They can also give you more accurate insights into each of the kits personalities.

Breeder
When looking for a breeding quality chinchilla there are a lot more aspects to consider.

1. Health is still your number 1 factor. Never breed an unhealthy chinchilla! No matter how insignificant the ailment may seem to you, in terms of breeding it is huge. Don't be irresponsible! Any responsible breeder will provide a health guarantee with their chinchilla. If they don't, be wary of their chins as they are pry hiding something from you.
2. Weight is another important factor. Most reputable breeders will tell you not to breed any chinchilla under 500g, with 600-650g being the preferred minimum breeding range. While still being a debatable point, breeding for small chins (save true dwarfs) is the same as breeding for extreme size. Pointless. You will find a few fanatics for it, but the only real reason for it is the breeders own personal preference. Like in any dog breed standard there are minimums and maximums for your pet. Consider 600-900g the min and max for your breeding chinchilla. One other thing I should mention is the difference between 'weight' and 'size'. Someone could have a good 'sized' chinchilla weighing only 600g sit next to an average 800g chinchilla and look comparable. You must also consider fur length, strength and body mass when looking at this area.
3. Fur quality is of extreme importance as well. This area is far too often over looked into today's splurge of 'backyard breeders'. Too many hobby breeders are popping up all over the place, putting 'pretty colours' together without any real consideration to any of the basics. The quality of the fur will often make or break the animal. At a show it's all about the fur. Things to consider when looking at the fur are density, strength, length, clarity, hue, texture, and veiling. A great page explaining this is: mutationchinchillas.com/a_glossary_of_terms.htm Fur quality is hard to explain words. The best thing to do it get out to shows, your local ranches and breeders and have them show you what to look for.
4. Confirmation again is something that a lot of the new 'breeders' (and I use this term loosely) seem to have forgotten. You can see some examples at the above link in point 3. When looking at a chinchillas' confirmation you want to see a 'brick'. When looking on from the profile, there should be little to no dip at the neck. The neck itself should be full to the body and be smooth to the chin of the chinchilla. Again no visible dip. When looking at the chinchilla from the top a similar shape should be seen. You want the shoulders to be as uniform to the hips as possible. See the below pictures for reference.
   

   
   Credit: Sunset Chinchillas

   
   Credit: A. L. Espenschied-Reilly

   
   
   
   

Which ever purpose is yours for wanting a chinchilla, do your research. Please don't support those who are in it just to try and make money or thought it'd be cute to have babies around. There are many good breeders around if you are willing to look. If not, then rescue. There are always chinchillas in need.

If you visit a breeder and you are uncomfortable with how their chinchillas are kept then ASK questions! Find out why they do what they are doing. If you leave and have a bad feeling then report them. Most authorities will only act of information if it is recent. If you wait a few months before coming forward your complaint may go unheeded. DON'T buy the chinchilla to 'take it from a bad place'. This is like supporting a pet store. They will only replace it with another. To them it was a successful sale, not a 'rescue'. If the chinchillas are not being taken care of, they will be removed from the owners care. You can also contact any local chinchilla rescues or breeders who take in rescues and see if they have any contacts that can help.