Well, hello there! The vet should know what to check for if you take them to a knowledgable chin or exotics vet. Mainly, teeth, parasites, malnutrition, just overall health.
Chins can easily be stressed. You'll need a nice quiet enviroment for them during the day, keep plenty of fresh water and hay as well as chinchilla pellets for them. Make sure you get the kind the previous owner had...changes in food can cause many problems and feed should be switched slowly adding a little more new food to the old over at least 2 weeks time. Give them plenty of chinchilla safe wood to chew on and wear their teeth down on...good choices are pine (untreated), willow, untreated apple branches and a few others that I'm not thinking of right now.
Chinchillas CAN have an evil side...I have a female that is still spraying when she gets freaked out, and as far as biting is concerned, they all test nibble EVERYTHING! You may want to do a google search for some websites pertaining to chinchillas. You can check mine at http://home.earthlink.net/~cutiepeach26/index.html
or another really good site for info is www.spoiledchins.com
You will find a ton of info and a lot of answers to your questions by checking out other breeders and chin owners sites. I also have a complete list on my site of things you will need to have on hand before you get your chins...so that will help you be prepared for their arrival. Also, check my links page for links to other great breeders with lots of info to share! Good luck and if you get them...pictures are a must!! Congrats! Rescue work is so rewarding!
Jade, posted above's site is www.chinnitude.com
She does have a lot of really good info and I recommend you read through it...you'll learn a lot!