That vs. Which

Your title was that vs which (not who). For all I know, "which" would be "proper," but for every day purposes either (that or who) is used. That said, "who," is probably formally incorrect. A "troop" is not really a "who."

If you want an authoritative answer, consult an expert, which I ain't.

In British English, you could use 'that' or 'which'. In US English you must use 'that'.

The choice is between 'that' or 'which'. A girl scout troop is a group or organisation, a thing, therefore, not a person, so we would not use 'who'.

The clause '...sells the most cookies' is a restrictive relative clause, one contains essential information about the noun that comes before it. Only one troop gets a prize. In British English, use either 'that' or which', to introduce a restrictive relative clause, but in US English, most authorities and guides recommend that you use 'that' to introduce a restrictive relative clause.

The other type of relative clause is a non-restrictive relative clause. This kind of clause contains extra information that could be left out of the sentence without affecting the meaning or structure:

Both US and British English agree that you must use 'which' to introduce a non-restrictive relative clause that does not relate to a person.

My new dress, which is made of linen, looks great with my blue sandals.

The horse, which she bought last year, is six years old.

Commas are used before and (if the clause is in the middle of a sentence) after non-restrictive clauses, so as to mark off the extra and inessential information.

"That". Generally the that/which choice hangs on whether you'd insert a comma or pause for an instant when speaking. If you'd pause for an instant when speaking, then the word after the pause is "which", otherwise use "that".