Basil, Dill, Rosemary, Cilantro, Parsley, Italian Parsley are our favorite herbs to grow.
We start all of our herbs in the greenhouse to give them a head start except for the horse radish which is a root vegetable and not a herb, we planted it and it is a permanent part of our garden but we use it like a herb. I do not know anyone that just chows down on a hunk of fresh horseradish like other vegetables.
Basil is very easy to grow and comes up fast, we like to grow the larger leaf variety because it is easier to pick.
You can just pick the leaves and chop them up and freeze them, then break off a piece as needed. Or you can pull the whole plant, roots and all and hang it upside down to dry, in a shady but warm spot, as with all herbs, basil will loose its color, flavor and nutrients if it is dried in the sun.
Parsley was one of the first herbs I ever grew, I think my mom thought it was a safe plant that I could eat when I was in the garden. Parsley is on the easy scale to grow, we like the regular curled variety and the non curled, Italian variety. We harvest it all summer and dry it for a little color in our food in the middle of winter.(Click on the image for a larger one)