My first steak

USDA Choice includes a wide range of variables but (even though it has less marbling than Prime cuts) it's usually high quality and, for the sake of argument, let's agree that the cut of meat was good.
Choice cuts are intended for dry heat cooking but the cuts that are from parts of the beef that get a lot of exercise (blade cuts, round, etc.) will be tough if you over cook them.
First, ONLY season the meat. You made a mistake coating it with butter. Butter has about fifteen percent water content. That's not dry cooking.
Second, you obviously cooked it too long. Medium rare means an internal temperature of about 145 degrees. Cooking a 1/2 inch thick piece of beef three to four minutes per side is too long - I'd guess your internal temperature was something closer to 170 degrees. That's pushing well done.
I would suggest that you try to find steaks that are at least an inch thick. If your steak was an inch in "height" your cooking time/method would have worked better. Even so, if you're cooking an inch thick steak, season it and let it rest for fifteen to twenty minutes to allow the salt to balance the moisture. Then, drop it into a "smokin' hot" cast iron skillet (or equivalent) and DON'T TOUCH IT FOR three minutes. Use your tongs to turn it over for another three minutes on the opposite side. Pop the pan into a 350 degree preheated oven for about five minutes. That should come pretty close to medium rare. However, use a meat thermometer to check the temp. and continue to use the term. until you get enough experience to judge time/temperature coordination.
If you want the flavor of butter on your steak (and who wouldn't) drop a pat of butter on it just before serving. Yummmm

If you want dry cooking you can also cook the steak in brown butter mixed with oil so you don't get too many of the burned milk solid compounds in your food.

Another way of determining steak doneness is to press it with your fingers. Different cuts of steak will feel different when you press it at different doneness, I find that a catchall guideline for doing so to be inaccurate. Tenderloins will feel different at medium than a striploin will feel at medium compared to a ribeye done at medium. The key to that is the more resilient the meat feels the more well done it is... constant practice will get you to the point where you will be getting it right without stabbing or slashing the meat.

As for times, if you are cooking just a half-inch thick steak two minutes or so a side should be more than adequate for rare/medium rare. As said above, such times are more appropriate for inch-thick to inch and a half thick steaks.

For flipping, just flip when you get a nice dark brown crust on one side. You can then let the meat rest when the centre goes up to the desired temperature.

Did it look like this? This is a New York Strip steak.

A flat iron steak?

"what tempature do I go by? " for medium rare you want 125, keep in mind the steak will go up a few degrees after pulling from fire so pull about 120 -122.

Um - does anyone really use a thermometer on steaks? It seems impractical.

A thermometer is extremely valuable. At work, I have one in my pocket at all times. It most definitely is a vital part of my professional tool kit. I wouldn't consider working without it. I use it to keep the health inspector happy. Do I use it on steaks, nah, never. Too impractical.

Stick it in from the thin edge of the meat. And they work great even on thin cuts like steak. Yes, I do occasionally do such a thing, more often with chicken cutlets though.

Phil