Just a few random thoughts:
Each of your suspects must appear to be more or less equal in the sum of the three parts of murder: motive, method (access to and knowledge of the murder weapon) and means (opportunity to use the murder weapon). Suspect A may not have as strong a motive as the others, but his access to and ability to use the weapon may be better, while Suspect B might have the weakest alibi but no knowledge of the weapon used, and Suspect C might have the best motive and history of using the weapon, but an apparently iron-clad alibi, or a physical or psychological impairment that seems to preclude his being the culprit. Proving whodunnit based on motive alone is difficult, since motive is subjective. What might drive me to murderous rage might not even annoy someone else. Your detective will have to either break an alibi or prove more eptitude with the weapon than a suspect claims to have, or dig out some error in the execution of the crime somewhere that the murderer forgot to account for.
If your murder weapon is something anyone can get and use - a telephone cord, or a kitchen knife, or a fireplace poker, for example - skill won't much matter. Forensics will tell you more than anything else, unless the killer knows to remove his or her fingerprints and is a frequent enough visitor to the site that other traces left behind wouldn't necessarily point to him or her. If the weapon requires more specialized knowledge, however, you need for any seriously considered suspect to have at least a rudimentary knowledge of its use, or access to clear instructions.
Not sure if I answered the question, but maybe there's something in there that you can use.