I agree with MisterSherbetLemon. There's no right way to do anything, every writer just has their own method of picking out a mystery and taking readers through it. I'm not an expert on mystery, but for me, a good mystery is one which I'm allowed to walk with the protagonist. As he slowly finds the pieces of the puzzle and solves the mystery, I'm right there with him. But that's just it, that's my opinion.
What I suggest is ask around to see what the general consensus is on mysteries. How do people like their mystery stories? Painfully obvious? Suspenseful till the end? Once you get a view on things, you'll be able to craft out a good mystery.
In regards to fight scenes, those don't show up much in mysteries, like Death Note was more of a psychological journey. It went on the battle of two minds. However, if you wish to show psychical combat, keep it to a minimum, and don't glamorize it. Remember, it's not a battle manga, it's a mystery manga