Well, where I live, my family has an electric stove (I know, Gas would be best), but what is the best type of pan or griddle for cooking BBQ style Steak and Chicken? I can imagine eventually buying an actual grill, but for indoor stove uses, what is there anything that is a half decent substitute?
My advice, if you are confined to indoor grilling--and I assume you don't have a fireplace--would be to invest in a good cast iron grill pan. There are several on the market, but I am personally enamored of products made by Lodge. Electric panini grills are something you might want to investigate, too.
You should check out Steve's book on Indoor Grilling. It's a fun book with a range of techniques and equipment. You'll be somewhat limited by your ability to vent smoke as well So you might be happier with something like a countertop grill next to a window.