As for choice of grill, I have the luxury of a two grill system. I start my meat on a super hot Weber grill, and always with natural hardwood charcoal. Lighting this type of charcoal can be a pain in the ass, so get yourself one of these, a chimney starter. Once you have the chimney filled with enough good lump charcoal, get some newspaper and put about 1-2 oz. of vegetable oil on it so the paper burns longer. Place the paper under the chimney and let it work. After about ten to fifteen minutes, wearing a fireproof glove or a thick oven mit, pour out the red-hot coals into the grill. Get yourself a long pair of tongs, and evenly distribute the coals. Let them set up and burn off any grim on the grate where the meat will be. Place the steaks on the grill with the longest points facing 2:00 and 7:00 on a clock. After about 2-3 minutes, depending on the thickness of the meat (this is for a steak about 3/4'' or 1'' thick) turn the steak to face 5:00 and 11:00 on a clock and cook for 2-3 more minutes: this is for pretty grill marks. Flip and repeat.
Now if you do not have a gas grill, at this point you want to move the steaks to a cooler part of the grill and turn the air system to closed so the heat dies down. I, on the other hand, have already placed a tray in my gas grill and turned the burners on the lowest setting. I place the steaks in the 250-300 degree gas grill to finish, much like I would for inside cooking on the stove and in the oven. If there are people who want to mistreat their meat and overcook it, then allow for a few extra minutes on the charcoal grill or longer cooking in the gas grill. Remember though, you have to add even minutes on both sides of the meat, or there will be uneven cooking from side to side.
Other foods that are to be grilled should can be placed on the charcoal grill after the meat is tucked into the gas grill. Things like onion slices, corn, and poblano peppers are nice on the grill, as well as hot dogs or hamburgers for people who are not looking for a steak. If you are considering chicken as well as steaks, you ought to cook the chicken first and let that carry-over-cook while the steaks are grilling. If you try to do the chicken after the steaks, it will take too much time to cook and the steaks will either get cold or overcooked in the gas grill. Remember though, all meat needs time to rest after cooking, so cook to 5 degrees under temperature and let the carry over time finish to a nice 128-130 degrees on beef for medium rare.
For any other questions regarding proper grilling techniques, please leave comments and I will be happy to answer them.