Knot of Thorns
The characters begin with nothing. They have no money, no weapons or armor, no gear, no animal companions of any sort and no material possessions besides tattered, dirty prison clothes. Equipment will be acquired in game.
Alchemists begin without their formulae book, extracts, bombs or mutagens. They must have access to an alchemical lab or chemicals to have any of these abilities restored.
Bards begin without their instruments.
Cavaliers have lost their mount. Presumably their mount was slain or given to another during their capture. It can be presumed that their week of mourning is already in the past.
Clerics begin having chosen all their spells for the day. They do not have their holy symbol or any material components however.
Druids also begin having chosen all their spells for the day. They do not, however, have their animal companion with them. Presumably such a companion was slain during their capture or escaped and awaits them outside. Regardless, such beasts would never be allowed inside the prison. Only if they escape from Branderscar prison will they have a chance to reunite with their companion or conduct the ceremony to acquire another.
Inquisitors and Oracles lack their holy symbol if they need one.
Summoners begin the game with their Eidolon un-summoned. They begin the game shackled so they are unable to perform the necessary ritual until they are free.
Witches, Wizards and Magi do not have their spell books, material components, familiars or bonded objects. They do however begin with a full selection of memorized spells from before their incarceration.