Herbs that I grow
From seed to go outside: Flat leaf & Curly Parsley; Coriander, Thyme, Marjoram, Chives (Garlic & Ordinary). Sometimes sow borage, dill and rocket. All these will grow outside up here (Moray, NE Scotland) in a sheltered south facing spot.
From Seed to stay indoors: Basil, Basil, Basil and more Basil and coriander...
I think tarragon is best bought as a plant - the best type of tarragon is French. The stuff in seed packs is Russian - not as good.
Never tried to grow Rosemary, Mint or Sage from seed. Mint will go 'mad' if not kept in check - our neighbour grows his in an old rubber track from a mini digger.
Another thing is location - we have the sheltered bed by the back door - handy for nipping out to cut a few herbs while cooking. Also, handy for getting the perennials which continue to grow through the winter - I don't want to tramp through the snow to get a handful of parsley or a bit of rosemary for the lamb.
Have fun
Sue