The very best hamburgers that I have eaten were cooked like this.
Form the patty with the most minimal handling you can use. You want a patty, but you don't want to overwork it. You want to have small pockets in the hamburger to catch and hold the grease instead of letting it run out. You want to leave air pockets in them, not compress them out of there. It doesn't really matter if the patty breaks into two patties, just arrange them on the bun to eat.
Don't mix anything in with the meat. When you do that, you are compressing the air pockets out. Feel free to sprinkle whatever you think you need on the outside of the patty. Mixing it in with the meat might give you some flavor from that, but you are destroying the natural flavor from the beef itself.
Minimal handling is key. If you overhandle it, the hamburger is second rate or worse.
Make the patty about 1 1/4 to 1 1/2 inches thick. Maybe a little dimple in the middle of each side. I often sprinkle some pepper on the outside.
Cook the hamburger in butter in a skillet over medium heat. Let the hamburger get the maillard reaction from the butter, not from burning the outside of the meat.
Never press down on the hamburger with a spatula. All that does is compress those air pockets and then the tasty greases have to run out and flavor suffers.
Cook to medium. Or medium rare if you prefer. Maybe medium well, but you will be sacrificing quality. Definitely not well done.
When you take it out of the pan, set the patties on a paper or cloth towel and let them rest for five minutes or so. This is to let the greases collected in those air pockets congeal so that they don't run out when you eat the hamburger. Do not set them on top of the buns unless you want soggy buns.
When I'm making hamburgers, I usually set the patties out to rest and let them rest while I toast the buns and wash the cooking utensils. Typically, it takes about five minutes to wash the pan and the spatulas and set them aside to dry.
Put he patty on the bun after resting for at least five minutes, add your condiments, and enjoy.
There are downsides. With things like steaks, you can get some bacteria on the outside of the steak but that is all killed while you cook the steak. When they grind it up for hamburgers, these bacteria can mix in with the patty, not just remain on the outside, and cooking might not kill all those bacteria. That's why the conventional wisdom is to make the patties thin and cook them well done. That's fine, but if you want excellence, you gotta take chances.
So, to sum it up:
1) Minimal handling of the ground beef. Form a patty, not a hockey puck.
2) Cook in butter on medium heat.
3) No compression of the patty. Ever.
4) Let it rest. Five minutes should do it.
Note that if you want bacon, you can cook it along with the hamburger. Don't overcook it.
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As for toppings, about 35 years ago I would go with either mustard or ketchup. At one point in time, I turned vegetarian for about two years due to a digestive issue I had at the time and didn't get much mustard. I craved mustard. Once I was able to start eating meats again, I only used mustard. I don't think that I've had ketchup on a hamburger in maybe 35 years.
I almost always sprinkle Cholula hot sauce on the hamburger. In fact, if I'm going somewhere for a hamburger, I will typically take a bottle with me so I can sprinkle it on the hamburger.

Years ago, I would often eat a hamburger at a hamburger restaurant that would by Cholula sauce by the carton. They would put one bottle on every table and then line the windows. In a month, all that Cholula sauce would be gone. Before that, I would use a habanero sauce instead, but now I keep it on hand and even carry it with me.
Onions, pickles, tomato slices, and lettuce on top of that.
As for the meat to use, I can get wagyu ground beef readily around here from someone I went to elementary, junior high, and high school with who raises it. They even deliver it. Or you can get it at the local grocery store for about $5 per pound. This is good, but it doesn't make the greatest hamburgers because it has been worked so much by their equipment that there are no air pockets in the beef to catch the grease. So I get better results from regular ground beef at the store.
Also, we can get some pretty good quality preformed hamburger patties around here. Again, these are overworked so much that there are no pockets of air for the grease to congeal in.
The most basic thing to remember is minimal handling. If you overdo it, you are going to get second rate or worse hamburgers.