Be careful of Chinese food, as well.
Most soy sauce for example is made from wheat (How they get soy from wheat I don't know) check the labels of every thing you will use....you can get gluten free soy, but you need to look for it.
Another thing to watch out for is cross contamination.
Neither my wife nor I are celiac, but her cuz is.
When she comes over, we use a new tub of marge, a new everything in fact. She is so sensitive to gluten that even a crumb of ordinary bread will put her in hospital.
As an aside, gluten free cake mixes are yuk. I found that substituting sufficient eggs to replace water (400g mls or so) beating the eggs til fluffy and folding into dry ingredients makes a rather nice sponge out of the affair.