You also want to get a coarse grind. Finely ground meat can become soft and mushy, making the patties hard to work with and more likely to fall apart on the grill. This is also the reason you want to be careful about what you put in the patty. Large pieces of onion, whole cloves of garlic or other smooth things can make the patty unstable. Finely chop vegetables and mince the garlic cloves. Also, avoid working with the meat too much. Fix it up, form your patty and leave it alone.
Moving away from beef, things like ground lamb, pork and ground sausage work well also. I've found that ground turkey can be difficult to work with because it can get so soft. The best way to deal with this is to add dry breadcrumbs to the meat. It will soak up the excess water and make the patties easier to work with. This is also a good trick if you like to added things like steak sauce or applesauce to the meat.
Now while other meats also make a great burger, mixtures of meats make a fantastic burger. Try mixing 3 parts beef with 1 part sausage. Or you can add a lamb flavor by mixing equal parts beef and lamb. But remember when mixing meats together or in just preparing the patties for the grill, the more you handle the meat the softer it will become. Mix gently and as little as necessary.
Once you have your patties ready for the grill you need to know a few things about grilling the burger. If you want step-by-step instructions, I have that on a separate page. Start with a very hot grill, as hot as it will go. Get everything ready and quickly lift the lid and gently place the patties on the grill. When the raw meat hits the hot cooking grate it will stick. It will seize the grate for dear life. If you try to turn it too early the burger will fall apart. The secret is to flip the burger the second it releases.
The process here is that as the bottom of the patty cooks the grease will create a non-stick surface on the patty and the heat from the grate will char the meat, separating it from the grate. At this point you want to lift the lid again and flip the patties, preferably to an unused part of the cooking grate. At this point the process will repeat. When the burgers have released again, flip them again and turn down the heat. It should only take about 1 minute per side to release from the grate. When you have flipped for the second time continue grilling for about 2-3 minutes. At this point there should be no pink left. Flip a third time and continue until done. This should be only about 2-3 more minutes. Remove the hamburger patty when done and let sit for a minute or two before you serve.
If you follow this plan you should get the perfect hamburger. From here you can build on with all the fixings.