Brain members as a category tend to be key strategists or leads for a team. Their strengths play into the knowledge they bring to the table and their abilities to out think any kind of puzzle challenges they come up against. One year the Agon was a massive labyrinth filled with monsters and riddles, so their importance to the group is not to be underestimated.
Brawn is typically the tank combative role. They do a lot of the heavy lifting when it comes to fighting, and a group's' offensive strategy tends to be built around them. If there is not at least two on a given team, they are in trouble.
Support is a more complicated category, but these team members have talents that lend themselves to acting as compliments to the group's more offensive members (ei: a child of Aphrodite using their ability to manipulate the emotions of the enemy to create an opening for their teammate to attack). Support members often times enter specifically with a brawn member because of their complementing abilities. Children of Demeter using their plant/weather based abilities to help heal or renew the group's supplies also hit into this category, as their role is literally to support the group.
Special is the broadest category, but covers members of the team with specialized abilities that may or may not give a team the winning edge. The visions of the future some children of Apollo have fit here, as well as the luck factor of Hestia's children, or Poseidon's ability to breath under water. That is not to say the team members in this role are incapable of combat, but their primary usefulness lies in their more unique talent.
*(On a side note, for the sake of flow and keeping the rate/ability to post up, I would suggest keeping the number of authors for each team at about 2-4. There can be exceptions of course, but I've found that is the magic number range that keeps a story from stalling out and dying.)