A well marbled steak with plenty of intra-muscular fat is essential. Think rib-eye (aka cowboy, tomahawk, cote de boeuf), or a cheaper cut like flank or skirt. Striploin is also beautiful on the BBQ but it needs to be cut really nice and thick.
Skirt steak is one of my personal favourites. You won't find it in the supermarket, but a good butcher will get it for you. It is known in France as bavette d'aloyau, but be careful as bavette is usually flank steak. Skirt is the well grained steak that is often used in Mexican and Chineses cooking.