I have a great sunroom with shelving to keep them going, do they have to die off in the winter or can I keep them going?
Annuals follow the seasons. They grow, flower, seed, and die. You can prolong their life a little bit if you nip the flower buds but you are in a race against time once they start trying to flower, because they are following the patterns of life for their kind. If you want a continual supply of an annual herb, you need to start new seeds on a regular basis to keep a supply. A much easier alternative, is to take advantage of that plant's cycle and grow several during their best time of the year and harvest them. Dry the leaves, flowers, or seeds, depending on the plant, and have enough until it's time to plant again. Some plants produce two different products. With the cilantro plant, the leaves are cilantro, the seeds are called coriander.
Perennials will grow more year round, but depending on your location, it is much less work to grow some of them as annuals. An easy way to tell an annual and a perennial apart, is an annual will have a soft stem, a perennial has a woody-looking, firmer stem.
Some perennials die back in the fall and come back in the spring. Being perennial doesn't necessarily mean it is in a growth phase year round, for some of them it means they will die back and come back.
Ginger, ginseng, and turmeric are perennials that you dig up part of the root, leave some in the ground and it will continue to live and grow more roots. It is toward the end of the second year before you can harvest any of the roots without risking the plant, but it grows pretty quickly. I planted a 3-inch piece of ginger in early April and it has put out growth in about an 10" inch area already and is getting ready to bloom. Ginger blossoms are not edible but they have an appearance similar to an orchid. I think that's their way of apologizing for the fact they are just about to take over your yard or garden...
Ginger and turmeric leaves are also edible. Both have the flavor of the root, but much milder. Ginger leaves are high in anti-oxidants, not sure about turmeric leaves. Ginger leaves can be added to cooked dishes and in small amounts (due to their strong ginger flavor) can be added to raw dishes such as salads. Turmeric leaves can be dried and then ground for a milder flavored spice and coloring in recipes. Turmeric leaves are also wide and are used as wraps for foods.
There is such a variety of herbs (leaves) and spices (roots, seeds, flowers and bark) that no one answer for growing plans works for them.