I think some weapons in the Book 1 category are more useful than others if the player is closely following the timeline.
- Water weapon for an easier Doomkitten and a large amount of fire-immune enemies that hinder Mage's rotation
- Fire weapon for Frostscythe and a decent amount of fire-weak enemies
At low levels, Mage benefits more from boosting Ice Strike -> Fireball with a higher damage weapon than spamming Attack with a lower damage, element-appropriate weapon.

Sir Jing's and Legendary Magma:
It is possible to reach the Hydra at Level 4 by not deviating from the timeline, which devalues Legendary Magma. Undead Assault has fire-weak enemies, but default weapons can deal with them. In addition, Legendary Magma staff and dagger are more unstable than the sword, and Mage benefits less from the weapon's element. For these reasons, I would get Sir Jing's weapons to breeze through Hydra and skip Legendary Magma to buy Fractured weapons instead.

Yulgar's Forge weapons:
Level 7 nature and Level 10 metal weapons are immediate upgrades to their Level 5 nature and Level 9 metal counterparts. However, a level-appropriate weapon would out-damage these forge weapons once enemies weak to nature and metal are encountered.

Warlic's Shop weapons:
Level 3 and 7 versions are quickly out-damaged by level-appropriate weapons against light-weak enemies. Level 14 version could be worth the price against the Vampire Tower. In both cases, inviting Artix(1) or Artix(2) instead is free.

Fractured Blade I:
If a fire sword is not needed at levels 8 and 9, Dragon Axe is slightly stronger for the same price.

Marsh Madness weapons:
A large number of weapons from this quest have low or unstable damage ranges compared to weapons from shops. Finding the appropriate base class weapon is another obstacle. It seems more time efficient to grind for gold instead.