The recipes below will feed about four, but adjust up or down as necessary. The first recipe in each category is the main recipe, then the two that follow are variations. Salt and pepper are assumed.
Mashed dishes are best made with russet varieties, and new potatoes are better for cooking in fat. (Use the latter type of potato for the labor-intensive Tater Tots, which are little short of a revelation.) You can peel the potatoes in these recipes or not; thin-skinned potatoes, especially, are just fine with a good scrubbing (use a brush).