Isa, most grits are made from white corn, so if you can find a white, medium grind cornmeal, then yes, that's grits. If you want to taste the basic grits, get a box of Quaker - quick are okay, but definitely not instant!
Then, once you have an idea of what the 'traditional' is, do try the stone ground grits, as elakin suggested.
Traditionally in the South, they take the place of home fries or has browns on the breakfast plate; look here for a recipe from the Honorable Floyd Spence, US Congressman from South Carolina: http://www.virtualcities.com/ons/sc/gov/scgvfs1.htm
And this is my own grits souffle recipe:
CHEESE GRITS SOUFFLÉ
3/4 cup grits
1 cup grated sharp cheddar
3 eggs, separated
1 ½ tsp. cream of tartar
¼ - ½ tsp. cayenne
Preheat oven to 400; Grease a 1 ½ quart soufflé dish.
Cook grits according to package directions. When grits are cooked, remove from heat and cool slightly; beat in cheese, egg yolks, salt/pepper, and butter. Whisk egg whites til foamy. Add cream tartar and whisk til the whites form stiff peaks. Fold the whites into the grits and cheese mixture, and pour into the soufflé dish. Bake for 30 minutes, or til the soufflé has risen and is light to golden brown on top. Serve immediately.