This is a very important question where Tarte Tatin is concerned. Pick the right apple and the result is a glistening, golden presentation of cooked apples on a rich, crispy base. Pick the wrong one and you get a smear of applesauce on a sodden slab of dough. The difference can be that dramatic.
In general you’re looking for a firm apple that is also sweet. Golden delicious was a popular choice of yesteryear, and it’s still the go-to apple for a lot of bakers (it’s excellent for baking and easy to find). Lately, Gala apples have become popular for tarts, though I have a hard time understanding why…they tend to keep their shape (mostly), but to my mind lose an awful lot of flavor in the oven. Other decent choices are Jonathans and Jonagolds, Winesaps and Newton Pippins. Best of all, if you can find them, are Red Romes, also known as Rome Beauties, probably the preeminent baking apple.
Avoid at all costs Red Delicious and McIntosh or anything labeled a “cooking apple” since these types break down to mush with heat. The Granny Smith, though it’s the first apple that pops into most peoples’ minds when you talk about firm apples, is actually a rather so-so choice, for reasons I’ll get into next.