One of the most important elements in your mystery novel is your detective. Depending on the type of book you're writing (police procedural, thriller, cozy), your detective might be a member of the police department or a gifted amateur who unwittingly becomes involved in your case.
If you plan on writing a series, your detective's personality needs to be one that you can explore over the course of several books. There are many wonderful mystery series featuring the same detectives that you can read. It's nice to have a sense of how other authors create interesting characters for their readers to enjoy book after book. Interesting sleuths include: Sir Arthur Conan Doyle's Sherlock, Colin Dexter's Inspector Morse, Agatha Christie's Hercule Poirot and Jane Marple, P.D. James' Adam Dalgleish, Raymond Chandler's Philip Marlowe, Anne George's Southern Sisters, and Nancy Atherton's Aunt Dimity.
M.C. Beaton's series feature two intriguing detectives: Hamish McBeth (a police constable in a Scottish village) and Agatha Raisin (formerly a busybody, currently a private investigator.) Hamish is a lovable officer--a gangling man who loves his village and desperately tries to prevent his own promotion (which would mean he'd have to leave the place he loves.) The readers tune in each book to check in with the recurring characters, see what's happening with Hamish's disastrous love life, and see how he plays down the fact that he has solved another case. Agatha Raisin, on the other hand, sometimes causes as many problems for the police department as she solves. It's fun to pick up a new Agatha Raisin book and see what trouble Agatha is in this time.
If you do choose to have an amateur detective, make sure that he or she is involved in the case in a natural and believable way. It's a stretch to believe that the sleuth just decides to play detective one day, for example. It makes a lot more sense that they would become involved if they or someone close to them is a suspect (and they want to clear their name) or if the victim was someone important to them.
It's nice for the detectives, amateur or professional, to have their own foibles to deal with. I loved it when even Christie's brilliant Hercule Poirot had faulty reasoning or made an error. Of course, he always figured it out in the end, but when he took us along on a red herring it was always fun.
Some publishers and agents are looking for books with specific hooks for the readers (this is especially true in the cozy mystery genre.) Does your sleuth also do crosswords? Quilt? Scrapbook? Hobbies can be tools to reel in readers.
In Christie's books, Poirot usually explained his reasoning and unveiled the murderer in a room full of suspects. That's less common today in mysteries. The reader is more likely to find the detective locked into a dangerous confrontation with the killer at the book's denouement. In a police procedural, you might find a similar situation--perhaps the police are desperately trying to locate the murderer (once they discover his identity) before he kills someone else. Or maybe the police have realized who the killer is at the same time they're recognized that a particular person close to him will be in danger.
Whatever personality and foibles you create for your detective, remember that they can help to make or break your mystery novel.