Worth growing
Mint of both kinds, lemon balm, lemon verbena, chamomile, sage, thyme, rosemary, tarragon, hyssop, fennel and nettle. All are easy, all are markedly better fresh or freshly dried than bought, and several are hard to buy in good condition at any price.
Not worth growing
Anything whose value is in a root that takes years — ginseng needs six and exhausts the soil for a decade afterwards. Anything tropical, unless you have the climate. And anything where the processing rather than the plant makes the product: rooibos is oxidised in heaps, mate is dried over fire, and a garden plant gets you neither.
The one that cannot be grown from seed
French tarragon is a sterile clone propagated only by division. Seed sold as tarragon is always the Russian sort, which is coarser and has almost none of the anise. This catches out a great many gardeners once.
Drying what you grow
Shade, moving air, and low temperature. The aroma of most leaves sits in surface oil glands and heat drives it off, which is why an airing cupboard beats an oven. Material that crumbles rather than powders, and still smells of itself, has been dried properly.