For kids, I'd say ham, but make sure it's a sweet type; kids tend to prefer honey, brown sugar, or maple-glazed hams over saltier types like black forest. Same thing with turkey, and I'd say you would need both; ham is popular but could trip you up on religious grounds, especially if you are not aware of the faith practices of all the attendees. Best bread for kids for cold deli sandwiches is hawaiian rolls (do you sense a theme here, LOL?)
The best vegetarian sandwiches I've found for kids are grilled cheese with apples (we use a panini press and spray margarine to grill them a few minutes ahead; no issues about brown sliced apples that way.) They are best made with gouda or mild cheddar on a hefty whole-grain wheat bread. Put the apples in-between layers of cheese for the best result. Kids LOVE these in my experience; even the non-vegetarians like them. We grill them whole, then slice them into quarters and put them on the food table just before letting the kids loose. (There really are not many good cold options for kid's veggie sandwiches, because most cold veggie sandwich options are fairly sophisticated. If you've got vegetarians in the group and heating something isn't an option, expect them to wipe out your fruit tray really quickly.)
Now then, my actual favorite sandwich? No contest, a shrimp po-boy, followed closely by a roast beef debris po-boy. My favorite deli sandwich is peppered turkey with asiago cheese and chipotle mayo.
PS: Now let's not turn this friendly thread into a chicken salad recipe rumble (I swear, chicken salad recipes have to be one of the most controversial non-political topics around; every time anyone mentions it, arguments begin.). For those of you chicken-salad fans not lucky enough to live in (or near) the South, I'll leave you with the menu for the 12 different varieties sold at Chicken Salad Chick:
https://www.chickensaladchick.com/our-food/restaurant-menu/