You want to keep the meat and grinding equipment cold during grinding so you don't get "Fat Smear" from the friction of the blade as it heats up. You can grind hamburger meat twice, but personally I only grind it once. I like Chuck as my main meat, but have added Brisket and other cuts with good success. Try to stay with hard white fat for grinding, and trim off all silver skin or other tough connective tissue that will get jammed up in your blade.
The key to tender burgers is to handle the meat as little as possible. The more you mix it, grind it, knead it, etc. will change the texture of the meat to more of a sausage-like texture.
I loosely pat together balls of ground beef trying to keep the same size and then push them down into patties. It doesn't matter if the edges have some splitting, all is good. Thick patties for the grill and thinner patties for the griddle. I never add eggs and all the other stuff in various recipes, I want it to taste like Beef!
