Warrior — economy
Warrior monetizes health better than any other class. Each Health Potion is +30 max HP, which compounds into more room-mistakes you can survive. Damage upgrades are still useful, but they're priority 2 below floor 10.
Archer — economy
Archer wants Attack Boosts early. Every +5 damage at a fast attack speed scales into a noticeably faster room-clear. Health is priority only if avoidable hits happened on the previous floor.
Mage — economy
Mage starts at 65% HP — Health Potions before floor 5 are almost mandatory. Once HP is stable, Mage gets the most out of enchantment levels per gold of any class.
Multiplayer notes
Gold is per-player. Each teammate should follow their own class priority. The party should wait through the shop — rushing past Continue while a teammate is still buying is the single most common avoidable wipe in co-op.