Do you use flour or cornstarch?

Flour definitely. Most turkey gravies benefit from long, slow simmering in order to meld the various ingredients into a superb blend of flavors.

A properly prepared roux, cooked until it is a pale tan, adds an extra 'nuttiness' to the gravy and ensures the gravy maintains the proper texture.

Cornstarch will release (as will arrowroot) if over-heated. It also does not reheat well for those glorious leftover turkey open faced sandwiches

I reserve the use of cornstarch and arrowroot for more delicate sauces rather than the heartier gravies.

I use flour. You can also toast the flour a bit on a dry skillet and then melt butter into it to form a paste called a roux. You can then add this directly to the drippings along with water to make the gravy, rather than mixing the flour in cold water and then adding that to the drippings.

Look up a recipe for rue.

I use butter, flour, milk, but the easiest way to make the gravy is (1) can of Campbell's cream of chicken soup (add water) and add sliced boiled eggs, salt, and pepper. VOILA!!! IT'S YUMMY! AND LESS WORK! AND MY FAMILY LOVES IT!