First I would always suggest private piano lessons over some music school. In a music school the main goal is not to teach music it is to make money... they have every incentive to slow things down.
The other reality of playing the piano is that some kids have trouble with the basics and others don't... don't be surprised if your son hits a wall at some point and you don't see rapid progression, its possible that he will hit that wall and then only progress at a more modest pace... The only things that really need to be focused on early on are how they are holding their hands and whether they are actually playing what they see or just playing by ear (which is sometimes easy for some people when they start but which will cause problems later).
As for the speed he is moving through the books... there is no right or wrong speed. He should be moving from one lesson to the next based on when he has mastered the lesson he is on... also don't be surprised if the teacher jumps around in the book. A good teacher will not just go through a book from start to finish as it is laid out because every student is different and it often makes more sense to move in a different order than what is laid out in a book (especially true once you get past the basics).
