Mostly, a LOT of space. Do some research on each of the herbs you want, and check on the mature size of each one. I think you're in for a shock! Of course, potted herbs will always be stunted to some extent, but when a plant wants to grow, it will and it's the below-ground bits you need to be concerned about, because a healthy root-system is what gives you a healthy plant.

You can forget entirely about trying to grow herbs on a window-sill. For one thing, you'll be hard-pressed to fit any half-decent-sized pot on your normal window sill. For another, your plants might get light, but it will be filtered through the glass, so your plant misses out on some of the valuable rays the sun provides.

You'll have difficulty providing good drainage for plants indoors. Excess water has to drain to somewhere, so people usually put a collection saucer underneath the pot. This means that the plants' roots are constantly in water - very few of the popular culinary herbs will tolerate this.

So - you'll need a special growing area which has a constant temperature to suit each of the plants in it; you'll need grow-lights; you'll need a solution to the drainage problem; you'll need adequate air circulation.

You can expect your plants to get attacked by assorted bugs and diseases, since they won't have access to Nature's own protective devices, such as predator bugs.

In short, plants weren't made to grow inside houses!

This question has been asked many times before. Try using the search facility at the bottom of the main page. Some people live in a climate where they have no choice but to have plants indoors - but they have to be satisfied with less-than-optimum plants.

The only thing that daisyduckworth doesn't mention is that it is very difficult to provide sufficient light for herbs inside. Most of them thrive in full OUTdoor sun, which is not something that we can duplicate indoors, even with artificial lighting systems.

Are you saying that you want to grow herbs indoors full time, or that you want to start them indoors for later planting outside?

Starting seeds indoors for outdoor planting is a great way to get a lot of plants for relatively little, get a jump on the growing season, and is the way to get uncommon plants/plant varieties.

In wintery locations, overwintering tender plants indoors is possible for some herbs but they need extra light and more attention to their needs than your run-of-the-mill "houseplants."

I guess a little more info on what you are wanting to do would help us give you more information. But as others have noted, growing herb plants full-time indoors is difficult at best.

FataMorgana

What are some good websites for herb seeds?

First you should figure out how much place the herb you're going to plant needs. If you don't have enough sunshine in your house, you need a grow light and a grow tent(determined by the area you're in). Suppose that the climate of your area is cold and try, a tent with air vents is needed. Fluorescent light is simply fine for normal herb growing. But if it comes to some special type of herbs which need longer sunshine time, a MH light or HPS light is needed, the former is for the first stage's growing while the latter is best for flowering.
I guess you don't know how to choose the right kits. I usually purchase online. Thelashop provides relatively completed gardening equipments.Just check it if you need to get.

Here is a link that might be useful: Growing tents, lights and others relevant

For seeds, try one of these:

Richters
Horizon Herbs
Nichols Garden Nursery
Pinetree Seeds
Johnny Seeds

FataMorgana

First question, which herbs are you looking to grow? Will they be in a south facing window with full sun? Do a search for water movement and read the thread specifically about soils by talpa. Herbs will do fine indoors just like any plant if given the right environment. Do as much reading as you can before you get started. A thing to remember is that container gardening is much different than in-ground gardening. Its not that difficult, just takes a little knowledge and understanding first.

The herbs that grow on window sill height tables by our 2 big thermopane windows facing south and east are Thyme, Basil, and Chives is just starting to come up. Oregano grew last year. You are all correct, they don't get as big as outside but it's enough to get us by through cold winters. The Thyme is in a clay pot so it needs water once or twice a day and I mist it when I remember. I am starting more seeds now that potting soil is for sale again.
Flatleaf Parsley is doing great in a cold basement window!
Needs less water because of the cold, around 65-67 degrees.

Are you watering it that much with standard potting soil? If so that is a recipe for disaster. You should be letting the soil almost dry completely out before watering. A good test is to stick your finger in the soil and if its dry dry up to your second knuckle then water. Of course, if you are using a gritty mix it is plausible for it to dry this quickly, but I wouldn't bet on it.