Best Class for Each Weapon
Counted on the passive tree: the class whose start reaches the most passives for each weapon within 20 points. Crossbows: Mercenary (20); Bows: Ranger and Huntress (12); Spears: Ranger and Huntress (10); Quarterstaves: Monk (14); Two Hand Maces: Warrior (10); Talismans: Druid (79); Bucklers: Ranger and Huntress (24). No passive names wands, and staves only appear on one ascendancy node. Patch 0.5.5, from the game files.
Weapon passives within 20 points, every class
Weapons the tree barely names
Sceptres: 1 passive on the main tree names them — Lord of the Wilds, nearest for Druid (15 points).
Staves: no passive on the main tree names them; the Disciple of Varashta ascendancy node Instruments of Power (You can equip a Focus while wielding a Staff; 50% reduced bonuses gained from Equipped Focus). Druid and Sorceress start with one.
Wands: no passive on the main tree names them. Witch starts with one.
How this is counted
For each weapon we take the passives whose text names it (crossbows also count Bolt, Ammunition and Reload; bucklers Parry; talismans Shapeshift, since every Shapeshift skill requires a Talisman) and count how many each class can allocate within 15, 20, 30 points of its start, walking the shortest path on the tree from the game files. Passives for a whole hand group (One or Two Handed Weapons, Block) are shown on each weapon's page but only break ties. Ranger and Huntress share a start, as do Witch and Sorceress. Each weapon page lists the nearest notables, ascendancy nodes and which class starts with that weapon.