Hi Ellie, Each herb has it's own characteristics.
Basil must have it's top pinched to bush out. It can be planted a little deep if you like. Basil leaves can be harvested as needed once your plant gets enough leaves to share. Keep the flower buds pinched off all the time. Once basil goes to seed, as an annual, it's only function is to produce seed then naturally die. I like to wash my basil very gently when I water it, and before picking a few leaves so I know that it's clean. Basil bruises very easily. If you bend a leaf in half you will see the fold darken alot. I love watching basil seeds when planting because after they get wet, they form a gel coat all around, amazing!
Rosemary, now here's a good one. It hates to be wet, but cannot dry out. Rosemary will tell you when it needs water bad when the tips of the stems turn downward. If this happens too often, you may see some stems dying back. If that happens cut the stem back till all the bad parts are removed. Rosemary is a perennial so you can enjoy the beautiful flowers. Some lore goes that The Virgin Mary placed her cloak over a rosemary bush and ever since the flowers remain blue. (Now there are lots of colors). Rosemary needs to be pinched some also to remain bushy. It can get quite large if you are in a good zone for it and it is happy. Rosemary is pretty hard to grow from seed, so a plant is a great way to start.
Thyme, oh it's such a darling plant with all of those tiny leaves. Thyme also should be pinched a little to encourage growth. Thyme does not too much water. Once thyme starts spreading (if it's a creeping variety) you can cover a little part of a stem with soil and it will eventually root. If it's an upright variety, give it a haircut now and then so it can bush out.
I use 14-14-14 Osmocote, about a teaspoon which should last almost a season, depending on conditions. Rain and heat will shorten the life of the time release fertilizer.
Now to the question at hand. I'll give you my answer, ok. I do not like to cut and eat the herbs too soon after purchase. I like to give them a little time to bush out and also wash the leaves when you water so that you can rinse away any possible chemical residue that may be residual. The herbs will start to mature and then you can decide to harvest some and use immediately (as basil in pesto and freeze) or you could tie a few sprigs together and hand to dry. Then again, you could chop up some and put them in ice cube trays to use through another season. If you'd like to try making vinegar with the herbs, there are many recipes online. If you decide to try infusing the hers in oil (use recipe), I suggest that you use within a few weeks and keep refrigerated. If you'd like to craft with the herbs, you could dip them in a paint then press onto a t-shirt, tablecloth, etc. Herbs can always be used as a garnish. I have also made wreaths with fresh herbs that looked so pretty. Some herbs you can make into a living wreath using 2 wreath molds, sphangum moss, etc. Same with topiary and such. Now they all need sun a good part of the day. How much depends on your latitude and zone. More information can be harvested by contacting your local extension service that every county has and ask for information that will be great info for your locale.
I'll be happy to answer any other questions. If I don't answer quickly here, feel free to pm me,ok. Enjoy those little buggers. BTW, they are not usually bothered by pests, but if they are, it's an easy fix for most. I like the natural products with pyrethrium, a flower. It's pretty safe but watching and washing them usually keeps them healthy.
Oh, I could go on and on....... like getting some oregano and call it your italian garden or pizza pots, or........