First rule for me is good meat. But for the love of pete don't buy wagyu or kobe or prime rib or filet mignon or some such crazy thing and GRIND IT.
My blend is: 50% well-marbled chuck, 23% oxtail, 25% sirloin, 2% pork belly (raw, uncured). If I can't get pork belly I use hickory or maple-smoked slab bacon (thick cut, meaning ~1/2" sections, one slice typically).
Good buns are impossible to find out here - how I miss thee, Martin's Potato rolls - so the best place to go for buns is… McDonald's. You can buy a regular hamburger 'nature' meaning it has nothing but bread and meat. Because they're special order, they're always made super fresh so they have't been sitting around for a while. Usually parents get them for picky eater kids. Anyway I keep the buns and if I had a dog I'd feed him the meat, but we just throw it out. The buns are pre-toasted which is nice, and they have a nice squish to them that supermarket buns don't. Also I hate sesame seeds on my buns.
Grinding: SUPER SUPER COLD meat grinder. Everything goes in the freezer; meat is cubed and put on a single layer on a baking tray and put in the bottom of the fridge (or kegerator, it's usually colder and has more even cooling). Grind once, keep already ground meat in a mound in the fridge as you go. You'll have to stop every pound or so of meat because the grinder warms up, and you don't want that - the meat'll get mushy. Put everything in the freezer for 30 minutes and drink a beer.
Cooking: 8-ounce patties, about 6-7" in diameter, sprinkled with médon sea salt and a lot of freshly cracked black pepper. Freshly cracked is the important part, because pre-ground pepper tastes like death.
Vacuum-pack with a foodsaver and put into the boil kettle with a PID attachment set to heat the water oven to rare, I think that's about 160 F? Let 'em sit in the water oven for about an hour, but not longer than 90 minutes or so. Yes, this is a health "risk" because it's in the "danger zone" for temperature but: 1. I sanitize my grinder before use, and the meat I use is from farms near me and is usually super, super fresh. Because I'm grinding myself there's less risk for nasties. Plus, life has risks. I don't let it worry me.
The water bath is great because it lets me take my time in doing everything else - the burgers won't overcook because the cooking medium is the same temperature as the meat.
Finally, I'll set the BGE to "T-Rex," around 600 * F. Depending on how people want there burgers done, I'll leave them on for a little while or a long while. Do one side, flip, put on cheese, bacon, whatever other 'hot' condiments need to go on, then put on a bun with whatever people want. I always put my 'moveable' condiments underneath the slice of cheese so they get melted to the burger patty and aren't as easy to move around.
Sides are usually cole slaw and beans, but sometimes (like this Saturday) I'll do sweet potato fries seasoned with powdered cinnamon and powdered chipotle (or ancho, depends on the crowd).
My favorite burger is either: sharp cheddar, 'shake sauce' (google it), pickle, lettuce, tomato OR stilton blue cheese, extra pepper on the meat, roasted garlic, onion confit.