I call these the Big Four: Parsley, Sage, Rosemary and Thyme. Easy to grow in our area (southern California), common to find in pots, and tasty in recipes.
They can be beautiful in the garden or pot. Parsley is a deep, deep, woodsy green and quite pretty when it blooms in its second year of growth. Blooming Rosemary's pine-like leaves look frosted with sky-blue flowers when it blooms; some varieties have white or pink blossoms. Soft looking Sage grows in pillow-like mounds and throws some lovely flowers above the leaves. Tasty Thyme grows low, with tiny, tiny leaves, and is quite decorative when each branch is capped by a miniature pom-pom of dainty flowers.
These herbs are easy to dry. While a dehydrator will make a very easy task of drying herbs, drying can be done in an oven if you do it with care. I have dried parsley in my ancient natural gas wall oven quite quickly. As the oven is very old, circa 1965-1970 (as I said, ancient--not kidding here!), it has a pilot light which will keep the oven somewhere between 90º-100º F. Just about anything will dry quickly.
For best flavor pick these herbs just before they bloom, but don't worry, they will still have plenty of flavor if you don't. The day before picking you can spray down the plants to get dust off of the leaves. The next morning pick early and lay leafy branches in in mostly one layer on newspaper covered cookie sheets so that they will dry quickly. Then, put the sheets in the oven . My oven's door is braced slightly open and the herbs are stirred several times to ensure all properly dry to crispy. You can most easily separate leaves and twiggy matter after drying, then place leaves in storage containers, preferably glass jars . In just a day or so enough freshly dried herbs can be packed away to last for a year.
As Thyme has such fine leaves oven drying will keep them together well. Rosemary and Sage can be oven dried or you can go old school: gather picked branches in bundles of six and then hang them out of the sun in your house or garage/patio to dry; during our summers, this can be very quick. Make sure you pack your dried stuff into glass jars as soon as it is finished to keep your herbs fresh and clean. Store your packed herbs in a cool, dark, dry place.
Herbs carefully and properly dried with any method will be fresh, colorful and tasty. Additional bonuses of growing herbs for drying: you will have plenty of herbs for fresh use as well as dried, you will know they will be very flavorful, and you will have plenty to experiment with when cooking.
For a great instructional article from the National Center for Food Preservation (NCHFP), look here: Complete instructions on drying herbs from the NCHFP.