The Greeks believed that Thyme imparted strength and fortitude. Later, in medieval time ladies embroidered thyme on scarves for their knights to carry as token of bravery. Growing these three plants will provide you with a wonderful herb to accent almost any dish, even desserts. Lemon thyme can be used in your favorite sugar cookie or muffin dough, as well as in breads and fruit salads.
Caraway thyme is a aromatic accent to meats when roasting.
If you can only grow one thyme I would opt for the common garden thyme. It's hardy to -20 degrees, and can be used in countless recipes. You can use it fresh, dried or frozen. To grow thyme plant it in a very sunny, dry spot. It doesn't like heavy soils, or shade, but if given a sunny location it will flourish.