I grow herbs in the garden as I have the room and it is easier than looking after pots. The exact list varies over time as heat/frost/drought/acid soil/limited drainage constrain what will thrive at any time. That is the first thing I want to say, that there is a tendency for people to lump herbs all together, even to grow them together and wonder why they don’t succeed. Compare rosemary, basil and Vietnamese mint.
Rosemary: Mediterranean, likes neutral to somewhat basic soil, well drained almost dry in winter, hates wet feet, perennial woody shrub, deals with frost, not subject to pests much, likes full or part sun. Useful both fresh and dried but better fresh.
Basil: Fast growing, fleshy and soft, best treated as an annual, likes warm dry air but hates roots drying out, copes with most soils but will do better if fed, very frost tender, easily grown from seed or tip cuttings, likes full or part sun, can get pests. Not native to the Mediterranean but important to the cuisine. Useful both fresh and dried, each having somewhat different sensory qualities.
Vietnamese mint: Not really a mint but looks and smells a bit like it. A stalky vigorous perennial from south east Asia that likes warmth and dampness and does not like drying out, not fussy about soil. Frost will tip prune it but the roots will re-shoot in spring. Easily grown from cuttings and/or roots, it tends to run. Best grown in a cool shaded or part shaded part of the garden to reduce drying but like true mints will grow in full sun if you can keep it moist. No pests that I have noticed. Used fresh in dishes like laksa, useless dried.
So my first suggestion is if you want herbs to grow well don’t put them all together as what suits some will not suit others.
Others that I grow are broad leaf parsley, thyme, sage, lemon balm, lemon thyme, lemon grass, oregano, horse radish, mint, garlic, tumeric, chillis. {edit} My bay tree died, drainage not good enough.
I have grown tarragon, both French and Russian. These are quite different plants that grow in different conditions although they have similar smells. The French is too hard to grow as my soil is heavy and you can only amend/raise so many beds. I happen to think the French is one of the herbs that is better dried than fresh and I like sauce Bearnaise. The Russian grows easily but the flavour isn’t as good and it doesn’t dry well quickly becoming dull and insipid even in the tightest jar.
What do I do with them? Too long to recount details but a hint on each.
Parsley; broad has more flavour than curled, only used fresh, mainly on French, Italian etc foods. When abundant in tabbouleh, tabooli or tabouli.
Thyme and variants, sage; roasts and stews.
Oregano; mainly Italian, especially pizza. Another that may be better dried than fresh.
Lemon balm; summer drinks
Lemon grass, tumeric; SE Asian spice pastes, curry, laksa etc Not smoothies!
Horse radish; sauce for roast beef, fresh is so superior.
Mint; both occidental and oriental garnish, with lamb and in taboolee.
Garlic; one of the 5 food groups, essential to many dishes, can be used to improve almost anything except ice-cream.
Chilli: I grow medium strength chillis to use fresh in Asian food but also to make sambalan which keeps well and can be used to perk up a dish, as a side dish, or to the dedicated, to eat on crackers with beer.
Last of all a little gem, all you wanted to know but were afraid to ask: Gernot Katzer’s Spice Pages. A wealth of information of the history, growing and uses of herbs and spices. Currently has entries for 117 plants - drooling .