Weapons information can be found here.
Gear information can be found here.
Sundry information can be found here. (costs of items may differ in your campaign)
WIP below
Your character may purchase a set of equipment and items before you send them off into the world. Their starting Gil is determined by their Birth Trait, and can potentially be further modified by their Standard trait. There are two sets of starting equipment, cheaply made Onion Gear and more expensive Basic Gear. Onion Gear generally has no special qualities, but is inexpensive, while Basic Gear comes at a higher cost but with more features. In the case of weapons, they come with Materia Slots, and in the case of armor, they come with added Abilities.
Materia Slots are included in Basic Weapons, and allow your character to further modify their weaponry based on which Materia they insert. Materia are round, marble-sized gems that can either increase statistics directly or add certain effects to your weapon, whether it's to apply a status effect on hit or automatically cast a spell each time they strike. The statistics you earn from the equipment are to be listed under "Equip" on your character sheet.
Every weapon also comes with a Property that sets them apart from other weaponry. Properties can range from a simple increase to your character's Flow all the way to increasing their EVA score by their PA score, 1:1.
Warriors and Red Mages can equip Heavy Armor and Helmets which increase their DEF and HP but slightly reduce MOV. DEF directly reduces the amount of incoming physical damage on a 1:1 basis and is very important for tank characters. They can also equip Shields which raise DEF, MDF and EVA.
Monks and Thieves can equip Light Armor and Headgear, which only adds more HP and occasionally a small amount of EVA. It's not as good as Heavy Armor at directly reducing damage, but it does add slightly more HP than Heavy Armor can.
White Mages and Black Mages can only equip Robes, which usually offer no HP or DEF but do give significant amounts of MDF. MDF reduces all incoming magical damage on a 1:1 basis. Another feature of most Robes is that they offer a 40% chance at the start of every round to automatically give your character 1 MP, which is useful in allowing them to cast spells more often.
Note that Warriors and Red Mages are not limited only to Heavy Armor, and each job has a wide array of armor and weaponry that it can equip. Check each job's wiki page to get a better idea of exactly which equipment they can use before making your decision.
Previous: IV. Abilities and Ability Slots
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Next: VI. The Zodiac Board