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Like with any AP the general assumption is four players, right now my group is going through with 5 players and I've always said 5 is the sweet spot for any adventure. It lets them have every role covered with that number and then one extra for anything else they need.
A must have skill is Kn: Engineering so any class that can have that and commit some resources to it is good, especially one that isn't feat intensive because technologist is all but a required feat. In fact I plan on giving it to my players as a free feat later in the books to any that haven't taken it.
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All Adventure Paths run under the assumption of 4 players. 5 Players still often works out, while a 6 player party may call for a +1 to the CR of most (if not all) encounters by adding more enemies, in order to keep experience levels up.
Too many PCs, generally 7, though if your group is disciplined and doesn't hem and haw and have to look up rules on their turns, going over 6 is possible (barely).
For Must Have Classes, there's no such thing in Pathfinder. No class holds a capability that cannot be covered by at least one other class. What you want to make sure of is that the party has someone to cover every role. Characters should be able to cover several roles.
A general listing of roles can be taken as this:
- Martial (Deals damage in melee)
- Ranged Martial (deals damage at range)
- Battlefield Control/Buffing/Debuffing (keeps enemies from doing anything effective on their turn, ensures your party martials can do effective things on their turn)
- Healing (Mostly out of combat, and access to restoration spells to remove conditions other than HP loss is ideal)
- Textbook (someone who can make Knowledge Checks consistently, Arcana, Nature, Religion and Planes are the most important for identifying enemy weaknesses and strengths)
- Scout (Ensure the party is going into combat with an edge. Spots traps, disables traps and gets insight on the enemy)
- Face (Diplomacy, Bluff, Intimidate and to a lesser extent Sense Motive)
With these covered a party can handle just about any challenge with minimal expenditure of resources and time.