The short version
Animal Hospital progression runs on two clocks: your shift depth (the game escalates events and pressure as shifts advance) and your class levels (documented at 200 class EXP or 199 Robux for level 2, and 850 EXP or 299 Robux for level 3). The class roster itself keeps moving — June's Class Updates shipped the system and debut skins, July reworked nearly everything, July 25 added the Firefighter, and September's event reportedly added Scientist and Barista. The durable unlock order is therefore role-first: buy the class that removes your runs' repeatable failure, level it to its perk tier, and let cosmetics follow.