At most schools, one has to take a set of graduate courses which can last anywhere from two quarters to two years. There are also several other pieces of graduate school bureaucracy that require attention such as placement examinations or cumulative exams. These are really no big deal because they are mostly based on what one learns at the undergraduate level. I first had to pick someone that was doing research akin to my interests. Once the list is narrowed down, other factors come into play.
Group size is an issue.
The drawback is precisely the same one. I have found that having the P.I. s undivided attention can be somewhat distracting, especially when they are itching for results. In a large group, one sees the opposite effect. The professor has to pay attention to many people at the same time, and this becomes increasingly difficult if the professor also holds a high-ranking administrative position. Selecting the group size is all a matter of taste.