What to cook in what
The honest version of a cookware guide is short: a coating is for things that stick, bare metal is for things that need to brown, and iron is for things that need time. Everything below follows from that.
Eggs and pancakes
The one job where a coating is not a shortcut. Eggs stick to bare steel unless the pan is preheated exactly right, and on a weekday morning nobody is doing that.
Searing a steak
Nonstick coatings should not be pushed past medium heat, and a proper crust needs more than that. Stainless takes the punishment and leaves fond in the pan for a sauce.
Braises and stews
Three hours at a low temperature, hob to oven without changing dish. Cast iron holds heat so steadily that the pot barely notices the oven door opening.
Pasta and stock
Volume matters more than the surface here. What you want is a tall pot that boils a big volume without climbing the sides, and a lid that fits.
Serving it
Food goes from the pan to a plate, and the plate is what everyone actually looks at. Heavier stoneware also holds heat, so a slow eater gets a warm second half.
Furnishing from scratch
A first kitchen needs pans, bakeware and something to eat off, all at once. Buying them as one bundle costs less than assembling the same list piece by piece.
The one-pan answer
If a kitchen can only have one pan, make it a 10 or 11 inch nonstick frying pan. It does eggs, it does vegetables, it will shallow fry, and it will sear adequately if not brilliantly. The second pan should be stainless, because that is the gap the first one leaves.