Red Mage is completely fine, while i more or less main Red Mage since introduced a friend and i have cleared fcob with just himself as Red Mage and me as Warrior.
SCOB is a different story but i plan on trying again when Blu is out.

I think you should start with coil first and progress to other raids. Not sure if people still do Wonderous Tails but i always have seen parties for coil because of it.