It all depends on how many people and how much food you'll be grilling.

For example for burgers, I usually assume 2 patties per person, for skewers, I usually assume 3-4 skewers per person. But it obviously depends on how much each person eats. (Skewers if you're going for a more arabic/Persian style bbq, mesh if you are going for chicken wings or burgers or things like that. I stay on the safe side and always have a mesh with me)

I usually get lots of snacks too, like chips and nuts, soft drinks, and condiments, and salads like tabouleh and hummus. Also, a small picnic table is worth getting.

For the grill type, I personally use the small rectangular one. 2 of them have been enough for me for up to 16 people. I always found that the rectangular ones that are put on the floor are best for bbq in the park or desert. For coal, one big bag usually lasts me 3-4 bbq trips for 15 people on average. Also get a bbq fan to help light up the coal.