Meats are graded by the US Department of Agriculture, and are available to consumers in three categories: Prime, Choice, and Select. Prime, the best, can be hard to find, since it accounts for only 2% to 3% of the stock and is often scooped up by restaurants. But more and more supermarkets have a small selection of prime cuts, and a good butcher can procure it for you, too.
Given your relative inexperience in the field, you’ll want to start with especially tender, flavorful cuts; as these are the best for grilling, that works out well. We’d choose either a rib-eye steak or a porterhouse, which has a section of tenderloin on one side of the bone and a NY strip on the other. You could also start with filet mignon, but it tends to have less flavor, and because it has very little fat, can be cooked too dry by inexperienced grillers.
Most people would say (and we agree) that the steak will have the best flavor and texture if cooked only to medium-rare — that is, still red in the center. You’ll get the best results on the grill if the meat is at least 3/4 of an inch thick. If your grill is up to the task, you should start the steak over very high heat, let it cook for about two minutes per side, then turn down the heat or move it to an area of medium heat, and cook another two minutes per side.
If you have a meat thermometer (which, now that we think about it, is pretty unlikely), slip it into the center of the meat horizontally, and it should register a temperature of 140°F (60°C). You can also press the meat with your finger and compare the resistance you feel with that of the muscle between your thumb and index finger, when your hand is relaxed. If they feel more or less the same, the meat should be medium rare. Or, if you think it’s about done, take it off the grill and cut into it to see if it seem suitable.