What is the most efficient and safe medication for fibromyalgia?

There doesn't seem: to be any one that works for everyone. FM is one of those conditions that gets diagnosed when everything else is eliminated and there are still persistent, major symptoms. FM is usually treated symptomatically, so there are a wide variety of approaches--mostly with pain killers. Here's a starting point, but do more research: http://en.wikipedia.org/wiki/National_Fibromyalgia_Association

Antidepressants: may be used for chronic muscle pain disorders and are frequently prescribed for the management of fibromyalgia. While first line choices are the tricyclic compounds, an SSRI or other class of antidepressant can be substituted when side effects are intolerable.