I like your concept. This type of game is quite popular with casual game players if you use amazing graphics.
For example, Snark Busters is a detective story where the player essentially wonders around and clicks things and has high-quality graphics.
If you're making a full-length game - 8+ hours of game play - then I would recommend you don't start with this game because it could take you months to complete if you're doing everything yourself and learning along the way.
Perhaps if you start by writing a few short games to learn about Unity and gaming. An idea would be to take the puzzle elements you want to put into the main game and write a short puzzle game with those elements. That way, when you start on the big project, you already know how to program most of it and whether you like game development and Unity.