The classic Good Eats method for perfectly cooked ribeye steak requires nothing but a cast iron skillet, a kitchen timer, and some salt.
As far as I'm concerned, a perfect steak is one with a darkly seared exterior and an interior cooked not one degree past 130°F. Although this can certainly be accomplished on a grill or broiler, it's a tricky proposition at best — especially with a cut like the ribeye, whose melting lipids tend to cause nasty, soot-producing flare-ups in open-flame environments.
Your best bet is roasting, in which a hot, heavy, dense cast iron skillet does the branding on the stovetop and the relatively gentle heat of the oven finished the interior.
It can't be said enough: Remember to let your meat — especially that of the red variety — rest for about 5 minutes after it's removed from the heat. Heat is akin to pressure, and cutting into a steak before it's had a chance to cool is a bit like opening a spigot. Cover the meat loosely with aluminum foil or a metal bow