Hi. If you're still looking for a fairly foolproof way to make a steak, why don't you give my method a try? I actually combined two methods I came across, and the result is tender flavorful steak.
You will need a probe, one of those polder ones is best. The instant reads are ok, but you got to keep checking. Start off with the best steaks you can, Prime, choice etc. Look for marbling. You mentioned the right cuts, tbones, porters, ribeyes, strips.
First step is to salt your steak, one hour prior to cooking. Yes, one hour. To read more google Jadens Steamy Kitchen Salt Steak. yeah I can't post urls yet.
I actually do not put as much as that blogger does. I salt my steaks good, but only as much as I normally would anyway, I don't put a ton of salt then rinse later. I salt, then wait. What happens is the salt draws out moisture from the steaks. Then the moisture dissolves the salt and then after that, the meat draws back in this salt water. Makes for flavorful and tender meat. So after that hour, if it's dripping wet still, you can pat dry or just apply whatever seasonings you want. Lots of black pepper, maybe a tiny bit of garlic powder etc.
Ok, preheat your oven to 275F or your grill to roughly the same temp (lid closed after you light). Insert your temp probe in the middle of the steak (if your steak has a bone, I find putting it a bit closer to the bone is better than middle). If using an oven, place the steak on a cooling rack over a half cookie sheet, or improvise as best you can. You want it to be open below the steak. If you have a grill, just put it on the grates, over burners that are not on. Let the steaks come up to temp. You say you like medium? 100-105F is what you're looking for. If you like medium rare (please try it!) 90-95F. When the temp is approaching your target, preheat the grill if you're not using it already. You want it to be fairly hot, but not hottest. Medium hot is good (you can use a cast iron skillet here). If you are using the grill for the preheat then you have to take the steak out, tent it with foil, and get the grill hot as fast as you can. You want to be quick. Ok, once the steak hits around 100F, pull the steak (from oven or grill) and transfer to the medium-hot grill. Cook on each side for no more than 2-2.5 minutes each side. I guess since you don't mind more cooked meat, you won't worry too much if it overcooks, and if it undercooks just throw them back on.
You should have something close to medium. You may have to adjust several things after your first shot. And it seems like a complicated process but it's not. It's just a pre-salt, then a reverse sear. Both methods well documented at Cooks Illustrated. The presalt seasons and apparently tenderizes the meat. The preheat before sear does two things, dries out the surface of the meat (good for not wasting heat and improve searing/browning), and finally, the 1/2 hour cook time allows enzymes to work in overdrive to break down the meat. CI called them cathespins I think. It allows for an abbreviated aging process so to speak, in the oven, in 30 minutes. They tested a reverse sear with a regular sear then finish in the oven, and noted the difference greatly. They even recommend taking the steak from the fridge right to the oven, as it allows the enzymes to work longer. I don't always but I have. Oh yeah, your thick steak (get it thick!) will have only a very thin gray section in the steak, none of that thick band of gray we all hate.