Baked potatoes and consequently loaded potatoes (twice baked), I find are best done with russets. This is how I have always had them, but your experience may tell you otherwise.
Mashed and sliced potatoes go to red and yukon gold. These are best boiled from what I have had, they mash so easily and cleanly too.
Cubed potatoes are good for a number of things: cheesy potatoes, casseroles, burritos, kitchen sink, and many other things you can think up. Many of these are much easier to make when the potatoes are already cooked, otherwise it takes like 3o minutes longer to cook anything. This makes them especially good as leftovers.
My favorite use of potatoes can be found here. This uses either shredded or cubed potatoes, already cooked. It’s such a complete dish, with lots of different tastes and textures mashing into a great bite every time.
One meal I really enjoyed in college was cooking potatoes and onions stovetop, cubed and diced respectively, and adding in cheese. Proportions are up to you, but roasting the potatoes stovetop with caramelized onions makes for some excellent cheesy potatoes. Bourbon chicken was an amazing addition to the dish, chunked or otherwise.
For casseroles, you can make almost anything, using a sauce as a base or cheese. Even better, you can use mashed potatoes, sliced, cubed, shredded, pretty much any way of preparation.
You could even take pre-cooked potatoes and mush them into a waffle iron to make waffle fries, or mash them and take palmfuls to make tater tots or similar (like the topping to shepherd’s pie).
Potatoes go well with creamy dairy like sour cream and shredded cheese, or gravy. Feel free to mix and match!