Sharp and mild cheddar. I'm making the sauce on the stove (flour, butter, 2% milk, cheese) and finishing in the oven. The sauce is grainy on the stove.
Harder cheeses like cheddar can be problematic and often separate leaving a grainy, oily mess. Try a blend of hard and soft. I get the guy behind the deli counter to cut a chunk of Land O' Lakes American cheese for my base, then add quality sharp cheddar (I don't need a lot), maybe some smoked Gouda, and whatever else strikes my fancy. (I like a four cheese blend)