Topping your hamburger is as important a set as grilling it. Of course there is the long standing traditional view of what to put on a hamburger, but you should always be ready to break with tradition, so dig into your refrigerator and pull out anything that will fit. Cut up the stuff that doesn't fit.
Living in the world of McDonald's marketing it's easy to be stuck on their formula for a hamburger. I can still remember the Big Mac rhyme. "Two all beef patties, special sauce, lettuce, cheese, pickles, onions on a sesame seed bun." Scary what advertising can do to you. Well, I usually use the onions, but that's about it. The secret to the perfect hamburger fixings is knowing what you like, so let me give you a few tips on putting it together. You can look over my recipes and get some ideas, but then you are on your own to explore your own tastes.
First of all let's talk cheese. Lots of people like to top off their hamburger with a slice of cheese while it's still on the grill. The cheese gets a little smoke flavor and nicely melted. However, I hate cheese dripping into my grill, especially a gas grill. So one tip is to take your cheese slices and trim them to the size of the patty before you start grilling. Make sure to trim the cheese slices smaller than the patties to allow for shrinkage of the patty. When the hamburger is done cooking, place the slices on the patty, close the grill lid and leave it there for no more than a minute. If you let it go too long the cheese will melt so much that it will run off the sides and make a mess of your grill. If you are done grilling you can simply turn off the grill and let the internal heat melt the cheese.
As for vegetables, slice them very thin. If people want a lot of tomato on their hamburger they can put on a couple of slices, but generally you don't want the hamburger to be too big to bite. Thin slices allows for good stacking without making a Dagwood sandwich. Put out plenty of toppings and let people assemble their own hamburger. At least a couple of times a year I put together a "Big Burger Bash" with a toppings bar for people to concoct their own perfect hamburger. It's always a big hit.