The recipe just says 'oats',but there's several kinds (instant,steel-cut,etc). Which to use here? What difference with different kinds?

In case you have a little extra time on your hands may I suggest toasting your oats before mixing them into said cookie dough? You can impart a little extra flavor, some je ne sais quois, with this method. Also, you can try rye or barley oats if you see them around-- sometimes a new oat can change your perspective.

I make an Irish Soda Bread/Brown Bread at Peels whose recipe calls for Steel Cut Oats, Oat Bran, Large rolled oats ( = Quaker) and small rolled oats ( = Quick Cookiing) and I adore all that oaty-ness.

I used Quaker rolled oats for the recipe.

For baking, I generally use old fashioned rolled oats - Quaker, typically. They're always in the pantry.

How they're used depends on what you're making: for cookies, the oats usually go straight into the batter as they are.

For breads or muffins, they're often soaked for about an hour in e.g., buttermilk before being combined with the other ingredients.

The kind of oats you want depends a lot on what kind of cookie you are making and a lot on how long they are to bake. It also depends on what kind structure and flavor of cookie or baked good you are after.
For most recipes for cookies that oatmeal isn't the biggest part, using quick oats is probably the way to go just to add some toothsome goodness :)
For your standard oatmeal cookie, "old-fashioned" oats will give you more structure so I would go with that. From there, I would just say experiment with different types and combinations to see what you like :)

Hope this helps!

If the recipe isn't specific, I'd use quick oats or whole rolled oats. Look at the cooking time and the manner of cooking. Quick oats will cook much faster, rolled oats will cook slower and give your recipe a heartier crumb. (Quick oats are essentially rolled oats, cut up a little bit.) Steel-cut oats take MUCH longer to cook and the recipe would have been specific if that's the type they wanted you to use.

http://en.wikipedia.org/wiki/Steel-cut_oats
http://en.wikipedia.org/wiki/Rolled_oats