What does dry red/dry white mean? When a recipe calls for a dry wine, look for a wine that is not sweet.
For a dry red, I tend to reach for one that has light to moderate tannins and is well balanced with fruit and astringency, like a cabernet sauvignon or a pinot noir. For hearty dishes, like beef or lamb stews, a Burgundy or zinfandel works as well.
For a dry white, sauvignon blanc is a good all-around workhorse. It has a good mixture of herb and citrus flavors to play nicely with delicate flavors like white fish or spring vegetables and enough creaminess to complement a chicken dish.
Do I really need to buy an expensive bottle? You might hear people say, "Never cook with a wine you wouldn't drink." It's true—to an extent. Although you don't want to cook with a poor quality wine, there's no need to get spendy either. There are many good options between $10-20.
What about cooking wines? Halt. Stop. Don't buy them. Cooking wines often contain extra sodium and are lower in alcohol and are not an equal substitute.