Our family LOVES Quesadillas. We eat them for lunch and dinner and for a simple snack. Often I just pull out everything that can be put in the quesadillas and then everyone gets to pick and choose. Sometimes I just do corn tortillas, but when I do flour I usually do those on a griddle that I don't consider a GF appliance and then I do the corn ones on a pan on the stove. It gets them all done faster and we can enjoy them while they are warm.
If I am in a hurry I just put the cheese & filling between the tortillas and microwave for about 30 seconds. If I have more time (or energy) I will cook them in a pan. For our mixed GF/non-GF family I usually cook the flour tortillas on a griddle and the corn tortillas in a pan on the stove. That way everyone's gets done about the same time.
*Some of our favorite fillings to add to the cheese are:
Pizza (pepperoni and any other pizza toppings)
Tomato & basil (fresh is best but canned & dried are good too)
Diced Chicken & basil
Black beans & salsa (sometimes we add corn)
These are our most common, but basically whatever is in the fridge has been made into quesadillas.