Generally, the rule used in English for pronouns is that you always use the objective form of a pronoun, unless the pronoun is the subject of a verb. If it’s the subject of a verb, then you use the subjective form (I, you, he, she, it, we, they). In all other cases—as the object of a verb, as the object of a preposition, or non-sententially—use the objective form (me, you, him, her, it, us, them). For example, the grammatical answer to the question “Who wants cookies?” is “ME!” not “I!”. By “non-sentential”, I mean pronouns standing alone, or in a list, but which are not related to verbs.
In the examples in OP’s question, the pronouns are used in a non-sentential list context—they are neither the subjects nor objects of a verb, so the objective case is the case that would be used.
Of course a lot of people get anxious about pronouns conjoined by and and think that it is always correct to use subjective forms, resulting in such hypercorrected monstrosities like “Give it to Jim and I”. I find using subjective pronouns alone to be just as monstrously ungrammatical as using them as the objects of prepositions or verbs: imagine someone answering a question “I!”.
As for ordering, it is traditional to list the first person last, in a kind of grammatical modesty, so I would say “Only three people signed up: you, Jim, and me”, but any ordering seems grammatical to me.