Potatoes are versatile; however, not all potatoes are created equally. When should you pay a little more and use red potatoes?
What gives potatoes different characteristics is how the starch molecules are arranged. When the glucose molecules are lined straight down in a chain, it makes up amylose and when the molecules branch out to the side, it forms amylopectin. The chains in amylose are easily broken when cooked and would be good for mashing, however, the high amylose content also gives it a "grainy" texture which I like to counteract with butter. The branched structure in amylopectin provides structural support so the potato can maintain it's form.
Russet potatoes (the kind you get in 5lb/10lb bags) contain more amylose. This is good when you want to break it apart as in mashed potatoes. It's also good for baked potatoes or potato wedges when you want a soft, tender texture. When used in soups or stews, it tends to fall apart. Imagine potato chunks that start disintegrating in curry or chowder.
Red/white/yellow potatoes are good for soups, potato salads, scalloped, or au gratin where it doesn't turn to mush after cooking. It's good when you want it to retain it's form.
In practice, you can use any potato for almost any purpose when it really comes down to it. It may not be best suited to that specific purpose, but can work if it's unavailable or significantly more expensive. For example, I actually like to use red potatoes for mashed potatoes because it doesn't become so grainy, it just means a little more work during food prep. Just keep this in mind the next time you make a dish with potatoes and want to get a certain characteristic.
One final note is to remove any sprouts on potatoes because they are toxic, but you would need to eat a large quantity to get sick. I would just be safe and get new potatoes if they start to sprout.