There is a lot of corn and rice in Mexican food cooking. Corn is used for corn tortillas and tamales. Yum!
In some parts of Mexico, mostly in the northern states, you will also find tortillas made from wheat, called "blanca" or "harina". But, corn is more popular.
Just think of all the things you can make using corn and rice.
My Chicken Green Chile Enchiladas are a perfect example.
Watch out for your sauces because wheat can be used as a thickener. If you make it yourself, you will be able to control that by using a gluten free substitute.