I have just planted a tray each of tarragon and sage seeds, and intend, once the seedlings are suitably developed, to transfer them to planters on the verandah, rather than to the main plot. What would people recommend as a suitable depth to ensure vigorous growth of the rootball and prevent them drying out too quickly in a warm summer?
Both those herbs tend to get a bit woody. I assume your aim is to harvest the leaves in which case your aim is to maximize top growth which can do by getting the plant pot bound.
Potting seedlings directly into a large diameter or large depth pot will allow the plant to grow roots at the expense of foliage.
I recommend re potting your seedlings into one pot size larger until you reach pots that are 8" to 12" in diameter. This process could take a few months.
You may be able to winter over these plants indoors by cutting them back hard and letting them regrow under high light inside.