All should do very well outdoors. They all require plenty of sun, and if planted in big enough pots should do fine. If grown indoors, they will be spindly, lack vigor, and any decent flavor and aroma. None of the ones you mention will grow very well indoors, unless you just plan to bring them in when the cold weather hits. Plenty of direct sun is necessary

They will all do fine outside this summer. As for surviving the winter:
-Basil is an annual, so it won't survive the winter.
-I know that parsley is a biennial, but I have only used it as an annual.
-Chives, oregano, and thyme should all survive the winter with no problem. Chives are extremely tough.
-Rosemary ... it depends. I have it in a large clay pot that I put in an unheated, glassed-in porch for the winter. The rosemary that I bought last summer overwintered well, but other winters, rosemary hasn't survived for me.

Other herbs that I have tried:
-Sage (the plain green kind): very tough.
-Lavender: I usually keep these in pots and move them into the porch for the winter, but I have grown some in the ground, too. I haven't found French or Spanish lavender to be hardy here. Some of the English lavenders (Munstead, Hidcote, and Blue Cushion)have been pretty hardy, though.
-Bay leaf plant: I bring this into the house for the winter. This is the third summer that I've had the same plant (it's now about four feet high).

BTW, you'll have to amend your clay soil. I break up the clay and mix in composted bagged manure and peat moss.

I'm in Michigan, so I definitely freeze in the winter. All will do well outside in the summer, be sure and plant oregeno in a pot or it will take over the garden and you will spend years trying to get rid of it. I grow my rosemary very well indoors on my ledge all winter. It's now about 4' and I use it. Basil will not grow indoors, plant it outside, pinch back all the flowers before it blooms and use it alot, it'll do better. What ever is left, use for pesto. I bring my Italian flat leaf parsley indoors every year and although it is a biannual, mine is 4 years old and still doing great. Thyme will do fine through the winter, it is quite hardy. Chives, one of my favorites, will definitely do well and will spread, not out of control, but a nice clump that you can cut through and separate early May. I love the chive flowers in cooking. They don't do that well indoors, although I try every year.

I have a good herb garden out back but was hoping to grow a few things in my new kitchen - now that I have 2 windows that get morning sun. I have lemon thyme, spicy globe basil, and thai basil. Should I not even put myself through the misery of trying to do them indoors?

Basils are usually quite tall (3-5 feet), unless they are the sort bushy types. They all need lots of sun all the time.