First, I'd probably go with A-brass in order to get information and minimize potential conflict. Zinc would also be a solid choice here, especially in compounding. Tin could be useful but I feel that F-tin would be better because it's more focused on specific senses. Pewter, iron, and steel would be useful for a more combat-oriented detective like Wax. Bendalloy and cadmium could probably be interesting, but not as good as some other options.
Then, F-zinc would be the best option for its increased mental capacity. If I were to choose zinc, then I probably should switch my other metal to A-zinc for compounding. However, copper could certainly be helpful. You could use it to memorize clues, information, interrogations, or anything else related to investigating crimes. Duralumin could help make connections quickly, and tin could obviously help with the investigation.
So, I'd go with either a zinc compounder or A-brass and F-copper.