What's the difference between dog societies such as AKA, AKC and APR?

My wife and I want to buy a west highland terrier, aka westie female puppy. When we look at ads they keep mentioning that they are registered with various societies. Can anyone tell us what the difference is between them? Are some more desirable than others? Any societies to avoid? We don't want to overpay but we don't want to get a problem puppy either.