It will all depend on the length of your stay at the site. In addition to the stationary staff, one or two wandering staff should be assigned to make rounds and check on youth as needed. If the site is exceptionally large, as are some amusement parks, an additional stationary staff member on the other side of the park is advisable. In order to really facilitate the use and placement of staff on site, it's a good idea to invest in portable two-way radios. These are also useful if more than one vehicle is being used.
Cellular phones are also useful, but primarily for communicating with people back home.
In any case, make sure that the food is kept and served at the proper temperatures and by the proper sanitary means. If you rely on a caterer or restaurant, make sure that you have confirmed meal times and the number of people to be served. Even if there is no meal planned, bring water and some small snacks. During summertime activities, heat, sun, and dehydration must be protected against with drinks, hats, sunblock and other means of cooling off. Likewise in winter, outdoor activities require children to be properly dressed and staff should have warm drinks, some blankets, and hand warmers readily available.