Buteo: you will get better results from your spuds if you plant them early, and at least six inches/ around 15cm deep. The reason for this is that new tubers form above the seed tuber, and if these new tubers are exposed to sunlight they will go green, due to the formation of solanine which binds to the chlorophyll in most Solanaceae, and renders their green parts poisonous. These are still perfectly good for next year's seed, just don't eat them. As the haulm (the green part) grows, keep piling up mulch around it so only the top few inches stick up out of the mulch, and more tubers will form along the stem. Keep the soil moist but not wet. If it's too soggy you will get fungal and bacterial rots.
Feed potatoes with compost and seaweed extract, which will help to prevent many diseases. My Gran used to grow them in a bed piled high with a mix of straw and seaweed, just a bit of soil at the bottom, and she got beautiful clean potatoes.
If you need to grow them in pots, bigger pots are better. Put a few inches of soil at the base, lay the spuds on it, cover with compost, straw and seaweed mixed together. Water them in well and don't water again for a few days. Do you have Gro-bags in America? Basically big garbage-bag sized bags, hessian or heavy plastic with ventilation holes, same mix you use in pots. Or old styrofoam boxes, like the kind used to ship broccoli. All these, like pots, can be put on a sunny porch to give you a few weeks of early start on the growing season. Except in exceptionally hot weather, potatoes like full sun.
