FWIW, if you're trying to witness to a muslim do it one on one, never in a group. In a group they will be compelled to defend their faith. Also, if you can get them to read Scripture it's the best way to get started. The Book of Luke is a great starting point.
I am intrigued as to why you'd say Luke in particular would be considered the best Gospel for them. It's my favorite Gospel--- I read it to my father after he lost his sight. It seems to be the richest in Holy Spirit action. And a goodly amount of attention to women!