There are two main things to consider when purchasing a fiber goat. The first is the health of the goat and the second is that it grows the type and quality of fiber that you want.
Give the goat you are considering a quick look over. You will want to see:
Prior to going and getting a goat it would be good to look at some fleece samples from that type of animal (colored or white, of similar age) to get a sense of what a good fleece looks like.
If you are planning to show the goat it may be necessary to purchase a registered goat, check with your advisor. Before making a purchase, ask the breeder about registration papers and how to go about transferring ownership. As you are looking for a good show prospect, you will want to study the CAGBA Breed Standard to make sure you select the goat that best meets your needs.
Remember, you are going to spend a lot of time with this goat - hopefully - and you will want it to be a goat that is pleasing to your eye and with a pleasing, enjoyable temperament.