I think red mage is basically dnd 5th edition bard; basically have buffs/heals but can pick offensive spells but not grand scale destruction like black mage does and they also have some utility skills/spells unique to them. They can wield some weapons (swords, rapiers, whips etc). If speak furry comfort zone I am fine at max 3 (past it is non-sexual interaction only). Anycase I think monk should be included on the warrior list (or rogue, or be included both list like red mage is rogue x mage class, white mage cleric x mage and monk is rogue x warrior class) and my suggestion for missing names are;
Red Mage = Fine with name, but they could also be bards basically (know unique song magic but can cast bit white/black magic and wield melee weapons and got bit utility; jack of all trades class which you can enter either through as mage or rogue).
White mage = Instead using same name as mage class (unless that's the point; can enter said advanced class either through cleric or mage career) it could be archbishop or simply bishop.
Some buff-based class = If white mage is advance class which can entered either as mage or cleric, then this class can be bishop. Or as evangelist (sort clerical singer class, as I feel if red mage does not hold song magic then evangelist be sort divine bard). Long cooldowns but long lasting buffs and while they 'sing' they are vulrenable but they can buff entire battlefields with multiple groups and buffs are very potent songs.
Saboteur = Witch class, basically specialize on curses and most useful vs numerous mobs than bosses as by default only few debufs work even on bosses at all. But debufs allow beat lots regular mobs easier and witch knows some healing spells but nowhere potent as other classes. But they can know lots status removal spells (remove curses, disease or other negative condittions).
Just my thoughts anyways :). Not intent it be complex but I agree it makes sense in first levels people got basic classes (warrior, rogue, mage and cleric) and then later can specialize to various advanced classes. Then there is job classes which can further increase player versatillity (crafting, gathering or some perk jobs like hunter job which increase drops from beasts which you slay and allows track beasts in woods better than anyone else or get even small pet as companion).