Learn Hardcore Russian: Вам стоит подождать минуту: сейчас администратор найдёт ваш билет. - You should wait a minute: the receptionist will find your ticket now.

Вам is the dative case of вы (to you). In Russian, advice/necessity is often expressed with an impersonal construction like кому (dat.) стоит/нужно/можно + infinitive.
So Вам стоит подождать literally works like It is worth for you to wait → You should wait (polite/formal).

What exactly does стоит + infinitive mean here? Is it about “costing”?

стоить can mean to cost, but in the pattern стоит + infinitive it means it’s worth / you should / it would be a good idea to.
It’s softer than a command and sounds like polite advice or a recommendation.

Could I replace Вам стоит with a more direct Подождите?

Yes. Подождите минуту. is a straightforward polite imperative: Please wait a minute.
Compared to that, Вам стоит подождать минуту feels a bit more like advice/explanation (often used by staff: You’d better wait a minute…).

Why is it подождать (perfective) and not ждать?

подождать is perfective and means to wait for a short while / wait a bit (and then stop waiting)—a bounded action. That matches минуту (a limited duration). (imperfective) is more like and can sound more open-ended unless you add context.