For best results, plant the tarragon, basil, and thyme in different containers. The plants need different growing conditions. Basil likes more moisture and richer soil than thyme. If basil has its own container, it is easier to replant without disturbing other plants. Basil is an annual. Thyme resents rich garden soil and thrives on neglect. Don't use a self watering container for thyme. Use a regular pot with saucer. There are pot feet to keep containers off of deck and balcony surfaces. I included a link to a nice garden supply place that has a wide range of pot feet, some pretty cool ones too! I've never grown tarragon so someone else can comment on its likes but I suspect they are different than basil and thyme. FataMorgana Here is a link that might be useful: Kinsman - pot feet

It _should_ survive just fine through a Georgia winter. But you can give yourself so insurance by propogation thru layering. Just take a few low, long twigs, bury them in the middle, wait a few weeks, and they should have rooted enough that you can cut them from the plant and pot them on your windowsill. I really wouldn't worry, though. Lemon thyme is hardy to zone 5b without protection.

Like many herbs, it will not take kindly to being grown inside.....especially in the winter. It's too warm, too dry, and too dark. Your stove light cannot provide the light quality (wave lengths) that any plant needs. If this plant were mine, I would cut it neatly nearly all the way back to the soil. Find the brightest window in the house and leave it. Water only when the soil has dried quite a bit to the touch. No more fertilizer! I would also not plant it outside until spring. Your plant will not adjust to the cold, especially after fertilization. I would inspect for and expect to find spider mites infesting your plant. If so, all the more reason that it will benefit from being cut back. Let me know about the mites. That could be why it looked so bad at the nursery. (Retail plant sellers are spider mite factories, lol.)

One rosemary plant (common) has been going great guns in front of my Arlington house for 4 years. Once in a 4-inch pot, it now sprawls more than 4 foot high and 6 feet wide despite repeated cuttings and samples given to friends. A couple of years ago, I was surprised to see it blooming in January--now I find blooms around 9 months every year. FYI one of the rosemary plants at Green Springs garden also starts blooming midwinter, but other well-established plants in the Bishop's Garden over at the National Cathedral remain unbudded until spring. I also have a couple of smaller and newer rosemary plants in a terrace garden that are doing fine, as are my sages. Only problem I've had with rosemary is with seeds not sprouting or damping off. Caution: I did manage to kill a creeping rosemary in Philadelphia a few years ago and couldn't revive a store-bought potted Christmas-rosemary-tree a couple of years ago, so I won't guarantee winter-hardiness of the varies subspecies. Lemon thyme seems more tender, perhaps the least hardy of the thymes. I've never had problems with my common nor creeping thymes--one common thyme survived for years on a Philadelphia roof deck until ignored by a really neglectful tenant. By contrast, I lost lemon thymes a couple of winters in a row here in Arlington. Thus, last winter I decided to split a spring-purchased plant. Turned out that part left in the ground survived the mild winter just fine, as did its 2 offspring in the coldframe next to the house, but one of the two plantlets kept indoors died--tricky to water them neither too much nor too little, or maybe just not enough sun (tho peppers and a couple of creeping geraniums overwintered successfully on the same shelf).