I love growing herbs! Propagating basil is really just as simple as cutting, stripping the lower leaves and keeping it in a water for a few weeks. Voila, a ready to plant basil and the mother plant will usually benefit from the trim.
The whole window will have a one foot wide window sill. I will have to show you the place to get a good idea of things. Basil planted in teacups for the kitchen, cheap and pretty teacups planted with fresh herbs on the window sill.