There are many different types of hives. The traditional "American" hive that folks think about is called a Langstroth Hive. There is the Warre Hive. And also Top Bar Hive aka as Kenyan. I'm sure there are many others that I am missing. The style of hive depends upon your style. As David puts in his book, there are 4 attitudes of bee keeping and there can even be a blend.
I know that this doesn't help answer your question directly. I'm new this year myself, but in research I was going to start with the TBH, but after reading I decided to go with Warre hives.
HTH
Matt