I've had lots of parties at the park and here is what I learned. One year, I ordered trays from Walmart, they have one that is all chicken - popcorn, tenders, boneless wings, etc. They were good, not terribly expensive, and something for everyone. BUT - the food experts recommend that after two hours out (inlcuding travel time) toss it because you have no real way of keeping them cold or hot. Last year, I made pigs in blankets and they were a HUGE hit. First, you can get disposable (but I re-use mine) chaffing dishes for like $10 @ Walmart, Sams or Big Lots and it includes the sterno! I made the food at home, with veggie dogs or hot dogs, and store brand "pop can" biscuits. If you buy the 4 pack of store brand biscuits - they are cheap, and you can peel the layers and they wrap a million dogs if you cut them in 1/2 or 1/3. Bake them at home, wrap them in the top section of the chaffing dish. Don't forget to bring bottled water to fill the bottom at the park. The park that we were at does have grills, but I didn't want my husband or me to have to be a slave to the hot grill, and I was worried that a kid would bump into it and get burned. I also brought mini bags of chips pretzels etc. (I've always hated going to parties and the chips are in a bowl or left open and they are stale quickly and grubby hands are digging around in there), any leftovers we then used for lunches or car trips over the next couple of weeks. I also had a veggie plate. The only accessories you need to bring then, are two tongs (one for dogs & one for veggies)and condiments. I brought a full size ketchup & mustard and individual mini dressings for the veggies - that way you don't have to worry about keeping open dressing cold, or double dipping, etc. If you rather, you could bring a full size bottle of dressing for people to pour on their plates, and put the condiments out on the table in a tiny cooler with ice left open, or a bowl of ice. Of course, there was a cooler with juice bags, capri suns, soda, water etc.... You don't have to fuss with 2 liters, ice and cups that way, and the left overs are easy to deal with too! The hot dogs like this were a HUGE hit, everyone ate them, they were easy to keep warm on site until they were gone, unlike the chicken tray the year before. With the chicken tray, after two hours, because I was worried about bacteria since there was no way to chill or heat a big round tray, I ended up tossing quite a bit :(, such a waste.
Of course, there was cake, and activities and everyone had a blast! Good luck, have fun!