If I had to choose herbs 'must haves' to put in a window box on the sunny side of the house I would include chives, oregano, lemon thyme and a creeping rosemary to drape over the edge. However, on the shady side of the house I would have a salad herb window box which would include wild rocket, chervil, French parsley and red mustard.
When growing herbs in containers, I have two important tips. The first is to use a soil-based compost, either organic compost. This is because there are very few herbs that grow in peat, and a soil-based compost retains moisture which is a must to stop containers drying out. I also advise watering in the morning rather than the evening because this gives the plants a chance if the temperatures are hot during the day, especially for containers grown in full sun. The second tip is to feed container plants weekly from March until September. This keeps the plants healthy, helps them produce leaves, especially on cut and come again salads. I use a seaweed-based feed, however you can use any proprietary feeds that boost leaf production.