You can assemble the burritos ahead of time and bake them just before serving. If they've been in the refrigerator, add about five minutes to the baking time.
Embellish your burritos with sour cream or salsa, if you like. Sliced tomatoes or rice would make good side dishes.
With the heat from the cheese, stay away from any serious, high-alcohol, low-acid wines. Try a white from a cooler growing area such as a Riesling from the Finger Lakes region of New York or any white from the Alto Adige region of Italy. A cold beer is a great alternative.