I bought a chinchilla on craigslist myself. Had terrible tooth problems that didn't show up until months later and I had him euthanized. I wasn't particularly sorry I got that one. He was a great learning experience because he was not tame and was difficult to work with.
If you go with a second-hand animal verify that its diet is correct. This is unlimited loose timothy hay and unlimited alfalfa based pelleted diet. This diet should not be the popular mixed diets with fruits and nuts in the pellets which can cause liver and tooth problems in the long run.
If the hair is not in good condition it can mean a number of things. It could be poor diet, habitual fur chewing, or a fungal infection. You'll want to have that diagnosed. Since you already have a pet I recommend a two week quarantine. Just keep the new chin in another room for two weeks and monitor its health. If it has fungus it will be less likely to spread to the others.
As far as neutering I don't recommend it at all. I know of three cases, one died, two were successful but suddenly stopped eating and had to be nursed back to health over a week after the surgery. One almost died and had to go back to the vet. Even if the surgery is successful you can still lose your pet from complications. You will have to monitor its food for three weeks and be prepared to syringe feed. Do not do this unless you have experience with caring for critically sick animals and are prepared to deal with morbid complications and the expense of multiple vet visits.
If you are up for the challenge that is fine too. I don't regret getting my chin from craigslist but now I personally would rather have a chin from a breeder that is hand raised and easy to work with going in, where I know its been cared for properly, and is unlikely to have genetic tooth problems.