For lack of a better name, I'll call the FFXIV stats that make up the regular fantasy game just that - regular. These stats are strength, dexterity, vitality, piety, mind, and intelligence. Three of the FFXIV stats primarily affect magic, the other three primarily affect physical combat.
These FFXIV stats are not purely combat-based, however. Stats also affect gathering and crafting. For example FFXIV piety helps fisherman (that pious lot) gather, and helps out alchemists and culinarians - when they're using their secondary tool. Below is a basic list of what each stat does and how it effects the non-combat disciples.
Strength - Increases physical weapon damage, increases shield block (damage prevented)
Synthesizing: Blacksmith (primary tool), Armorer (secondary tool)
Vitality - Physical defense, increase HP (For Disciples of War, 1 vitality = 14-15 HP. For Disciples of Magic 1 vitality = 8-10 HP)
Synthesizing: Carpenter (primary tool), Armorer (secondary tool), Leatherworker (primary tool)
Dexterity - Physical weapon accuracy, chance to evade, critical hit rate, parry rate (some weapons)
Synthesizing: Goldsmith (primary tool), Weaver (primary tool), Carpenter (secondary tool)
Mind - Magic spell defense, healing spell potency (+1 HP per 2 mind), increases MP (For Disciples of War 1 mind = 2-3 MP. For Disciples of magic, 1 mind = 9-10 MP)
Synthesizing: Culinarian (primary tool), Blacksmith (secondary tool), Weaver (secondary tool)
Intelligence - Offensive magic spell potency
Synthesizing: Alchemist (primary tool), Goldsmith (secondary tool), Leatherworker (secondary tool)
Piety - Magic spell accuracy (reduces chance attacks will be resisted), increases magic defense
Synthesizing: Alchemist (secondary tool), Culinarian (secondary tool)
Please note that while a given stat will obviously help some Disciples more than others, there may not be as much benefit to completely ignoring the other stats. For example, Vitality helps everyone out, by providing more HP. Dexterity may be somewhat useful for Disciples of Magic, since a few of their attacks are based off of physical weapon accuracy.