You need to ask her if she or kids have any dietary restrictions. Gives you a reason to see her again, tweak the menu, and shows that you care. Making a fancy burger/chicken meal only to find out she's a vegetarian would start things off poorly.
Absent some restriction, I prefer kabobs over burgers/dogs. Burgers and dogs seem lazy to me and you're trying to impress. A nice rice pilaf and fruit salad would make for a healthier first meal as she seems to care about her fitness. Maybe have dogs around for the kids as you could throw those on the grill if needed (I'm a Hebrew National guy).