I worked as a sitter in college, and I think it's totally reasonable to say "Please fix . . . . for dinner" as long as it's relatively straight forward, and simple.
I might expect a nanny to be able to look in the fridge and figure out what to cook, but I'd expect a sitter (i.e. someone occasional, who doesn't have a lot of experience with your kitchen or with what your kids will eat) to need more direction.
As far as what to cook, I think my kid would enjoy making his own pizza with a sitter, or breakfast for dinner with pancakes and scrambled eggs.