Just as there are several nations where the easiest way to instigate a dispute is to ask for the best way to make tea or coffee, in Serbia there are strong opinions on how to do barbecue.
First, as a general rule, nobody even tries to sell propane barbecues. It doesn't exist. The only proper fuel is charcoal, then firewood (with some strong opinions on what kind of wood is the best - oak, grapevine stumps, cherry, acacia, maple are OK, willow, conifers and few other soft woods aren't). The coal dust pressed into cakes (called briket here, probably related to bricks) and possibly doused with mineral oils and phosphor is not popular. It was pushed on the market in the seventies, but even then it was just clean dust without stuff added.
I haven't seen a barbecue with a lid, which is too bad - the lid is a nice invention. The ones you can find are mostly simple metal boxes with two grilles, frequently with hooks raised on the sides, into which you can insert a spit, big enough to roast a chicken on it.
Two most traditional meals are ćevapčići (see here but look into the expanded article in serbian) and ražnjići (kebab on skewers of either stainless steel or wood). The next in popularity is pljeskavica (literally, a clapper, a patty, as it's shaped by clapping hands), which only superficially resembles a hamburger patty. The ground meat is mixed with salt, peper and chopped onion. In some variants, a slice of cheese is kneaded in the middle of it. Sometimes, it's half the size with a cheese cube inside but somewhat thicker; then it's called a medallion (medaljon) - some chef's invention.
Other dishes, popular in restaurants, are various sausages, and bela vešalica (literally: white coathanger), which is a thin slice of rather white meat somewhere from the pig's back. And various steaks, of course - preferrably pork's neck or back. Meat from front or hind quarters isn't greasy enough and often comes dry after roasting. When in doubt, order mešano meso (mixed meat) and you'll generally get 3-4 different pieces, the best off the house grill. Some places have a leskovački voz (Leskovac train), which is a 4-5 dishes marathon, or some local variant of it.
The meat is mostly pork, then chicken; beef is not as popular. The recipe for ćevapčići, however, calls for a pork-beef mix.
The salad which goes with it is, traditionally, just raw chopped onions and nothing else, but that has changed. Now you can get pretty much any standard salad with it.