Choose storage onions (yellowskins, Spanish and reds) that are dry on the outside and firm to the touch. The skin should be papery, almost brittle, and the shape smooth, round or oval. Store in the mesh bags they're sold in for maximum air circulation. If kept cool, dry, and in the dark, they should last well for up to one month.
Bunching or green onions are meant to be used fresh. Look for smooth, firm, white bulbs and bright green tops. Trim immediately and refrigerate in a plastic bag for up to one week.
To peel cooking, Spanish or red onions, first score in several places, from one end to the other (if difficult, also peel away the outer layer of flesh). To prevent "onion tears", peel while holding the onion under cold running water; or briefly parboil, drain and peel; or boil or steam the onion whole if appropriate to the final preparation, and peel after cooking.
Bunching onions are easily peeled by gently sliding off the outermost paper-thin layer after trimming.
Onions are best chopped by hand (food processors easily reduce them to mush). Cut in half, place flat side down, hold at root end and make a series of parallel cuts. Turn 90 degrees to make several close cross cuts to produce finely chopped onion.
To make thin, even onion rings, peel and carefully slice off a thin piece halfway between root and tip end along one side. Roll onion onto newly cut side to rest flat, hold steady at root end, and slice.
Bunching onions are well suited to use raw and thinly sliced in salads, or as additions to cooked foods, especially Oriental and Asian dishes. They're also a delicious garnish for vegetable soups and with eggs, cheese and fish. Never overcook these delicate onions.
Spanish and reds can be used in much the same way -- in salads, sandwiches and simple stir-frys.
Cooking onions know no limitations. Use in stir-frys or slow-cooked casseroles. They can be baked, braised, boiled, grilled, and made into classic onion soup. They are completely cooked when the flesh is moderately tender. Slow, gentle cooking seems to bring out their sweet flavor.