Hamlet's first act is to grab Ophelia's wrist, stare seriously at her, and walk away. This act is not specifically "mad", but unusual. It is a good place to start because it does not call attention to his concerns over Claudius and Gertrude, and because it is subtle. He can build slowly from here and get worse as he goes.
I think he also chooses this because it allows him to express himself in some ways towards Ophelia. He is clearly uncertain about how to handle the "relationship" that is in flux between him and Ophelia. Focusing on her first could be a manifestation of that uncertainty.