I'm confused a bit but the comment but It could just be me misreading your post too, sorry...But I would like to add that I will be doing the same exact thing. May profession will be and investigator and teacher.
We don't know how investigation skill will work exactly but if it is as you say, I think being in a school with other professionals will be important. The criminal investigation skills just help you find criminals, but how would you know what stabbed the player without a blacksmith who knows about blades, how would you know the type of poison without being an alchemist, etc. You can of course learn over time but having others to consult will help.
Are you planning to be an investigative school or just a normal school have has investigation in it as well..