I have some herbs just poking up good and they are in 3" terra cotta pots. I got the "kit" from Staples in the clearance section at back of the store, and the brand is the same as the Chia Pets. They said to put the pots on top of the fridge, which is always a source of warmth. Now I have them sitting on top of the gas water heater, and turn them about twice a day. One of the most rewarding herbs to grow is the basil which grows quickly. Then I'm happy with the looks of the dill and the parsleyand the thyme. But I'm disappointed in the chives. I have better luck buying a pot already started. Rosemary is pretty to grow, but does not like wet feet. Very touchy to get it right with rosemary. My rosemary is outdoors in the flower bed with no protection, and it is doing great. For Christmas, my DIL gave us a hydroponics set up with auto feeding of 3 kinds of herbs. Again, the basil is exceptional, quite big enough to start pinching off leaves. When we redo our kitchen, the window over the sink will be replaced with a garden window for my herbs and smaller potted plants. It faces south, and by the time the hot weather arrives, the roof overhang should give this area a good bit of shade. Right now, it is a perfect spot for house plants I brought indoors for the winter. Here are a couple of pictures: If the fridge top works for herbs, it also works for birdnest fern and staghorn fern and nun orchids. This is the hydroponics thingy. A lot of trouble IMHO.

Here's some of my experiences growing herbs from seed. Thyme: the best for eating is Summer Thyme. It germinates best (indoors) with a heat mat giving consistently warm temps, and then after germination it grows quite slow. This can be started any time now to have decent transplants. Oregano germinates easy and grows a little quicker but would still be worth starting early as it takes a while to get plants to harvestable size. I've not grown winter savory, but I do start Summer Savory each year - this is a fast growing plant and doesn't require seeding more than 6 weeks ahead of frost when started indoors. Basil is another seed that benefits from warmth for germination. This plant most definitely will suffer from cool temps. Dill and Borage can be direct seeded. I've not grown any type of mint from seed, only from cuttings. Be very, very careful where you plant this as mint's main purpose in life is to take over the world. I've not grown Cilantro yet but I do have seeds to start this year. I'm planning to start them about mid-March and grow cooler rather than warmer. I like to grow herbs in pots which, I find, keeps the plants cleaner therefore easier to harvest. You can also then place the pot in conditions the herbs like best. Basil, Oregano and Thyme all like as much heat and sun as you can throw at them and dryish soil. I like to make an herb garden in a 3 to 5 gallon pot, covering the soil with crushed rock after transplanting, which helps keep the soil warm and the herbs clean.

Sage should do fine as long as you purchase the correct variety but as for mint you should be able to find a friend to donate a few shoots and Rosemary is best from a plant. I a few years you will have too much but should keep taking cutting for new starts in case your parent plant should suddenly die. They are easy to start cuttings in a pot kept in a light shaded area and the light soil should not dry out. This will change once the cutting takes off If you can find a friend who will give you cuttings that would be the cheapest way to go.

You didn't state your zone, so could be that they're drying out too much or too hot of roots in the pots. Try growing them directly in the ground or transplanting them to the ground sooner. They need nutrients & room for roots to spread. If they dry out in the pots they're toast. I grew herbs in pots for years, but with limited results from seeds. Used a variety of pots small & large, plastic, clay, glazed, metal tea pots, etc. Once I moved those same herbs into the ground WOW they spread a lot & the flavor improved. Probably because the plants were healthier. I've kept some in pots just for looks, but they're not thriving. The ones in the largest pots do okay. Oregano is growing well in a metal colander & a large steamer like you'd use for clams or pasta. Kind of funky, but I like the electic look. Also, have parsley in a plastic pot inside a large enamel pot with a tea cup & saucer on top as well as a large kitchen spoon & server holding the lid off to the side.