The most delicious, memorable potato dishes I have ever tasted have been, without fail, at Joel Robuchon restaurants. The chef takes the humble spud and makes it into something sublime. His pommes purée is one of his most famous creations, and to get something this rich, smooth and luxurious involves a lot of butter and forcing the purée through a fine sieve.
I have eaten that dish many times (sometimes with black truffles, which makes it even better), but more recently, at Robuchon au Dôme at the Grand Lisboa in Macau, I tasted his potatoes confit. They were shockingly good, like the most delicate, airy purée held together by fragile potato skin and so delicious they threatened to overwhelm the main focus of the dish, a roast guinea fowl.
Technique is important with these dishes but so is the potato variety. At regular supermarkets, you will probably find three varieties: the so-called baking types, which, when cooked, have a "floury" texture; "new potatoes" (which aren't freshly picked young potatoes, as the name would imply, but instead tend to have smooth, thin skins, and are waxy types used for boiling); and "all-purpose" potatoes, with a texture somewhere in between baking types and new potatoes.
It is a pity that there are not more on offer, at least, at reasonable prices. Occasionally I am surprised when, at the wet market, I find a vendor selling true new potatoes. Tiny (about 1.5cm) and misshapen, they look as if they have just been pulled out of the ground and still have soil clinging to them. More often, though, you have to go to high-end supermarkets if you want anything other than baking, new or all-purpose potatoes.
Each country grows different types of potatoes to suit its cuisine, although of course there is some crossover. The types used in France, such as the ratte (which, I suspect, was what I tasted at Robuchon au Dôme) are perfect for absorbing butter; certain varieties, such as the May Queen, are used in Japan because they hold their shape and take on the flavour of the other ingredients when they are simmered to make nimono, or stewed as a nabe.
Potatoes are known for their keeping qualities: in the olden days, in countries that depended on them for sustenance, certain varieties were grown in quantity, harvested in the autumn, then stored in root cellars and consumed during the winter. But freshly harvested potatoes, a lot moister than the ones that have been stored, are a rare delicacy.
Potatoes are now stored in conditions that keep them in better shape than the root cellars of yesteryear, but when you buy them you should still check them for quality. The skin should be tight over the flesh, they should feel firm, and there should not be any tint of green under the skin: the green is an indication that the tuber was exposed to light, and, if consumed in quantity, can be poisonous.