If you cook with herbs at all, start with your pantry to see what you use most. This is my pantry list.
Type of Herb | Herb | Frequency of Use | Current Supply |
Annual | Basil | Always in Italian red sauce, some pestos | ½ regular bottle |
Annual | Cilantro | Almost never – I don’t care for the taste |
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Annual | Dill Weed | Always in tuna salad | ½ std bottle |
Perennial but grown as Annual | Garlic | Used on steaks and other meats, in red sauce | ½ bottle powered |
Annual | Leaf Marjoram | Always in red sauce, some on herbed chicken | 1/3 std can |
Annual | Summer Savory | Used on herb pork chops or chicken, bean soups, chicken soup, red sauce | None |
Biennial | Common or Curly Leaf Parsley | Always in red sauce, often on pork chops, chicken, or in tuna salad | ½ std bottle |
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Perennial | Bay Laurel | Used to use in red sauce | None |
Perennial | Chives | On Baked Potato | ½ bottle dried |
Perennial | Rosemary | Always in red sauce and on herbed pork chops or chicken | ½ small can |
Perennial | Thyme | Sparingly in red sauce | 1/3 powered bottle |
Perennial | Oregano | Sometimes in red sauce or other Italian dishes | ¼ bottle |
Perennial | Sage | Always in red sauce and gently with herbed chicken | ½ std bottle |
Perennial | Summer Savory | Hearty bean soups or stews, rich meats | None |
Perennial | Tarragon | Used for Chicken Tarragon | ½ std can |
From my chart of 16 herbs, I would start with basil, curly leaf parsley and Italian parsley, leaf marjoram, sage, rosemary, tarragon. Then add dill, both summer and winter savory, garlic and bay laurel later.
Checking the pantry is just my method, you could also research what is easiest to grow indoors or what looks like fun. Google - what herbs are easiest to grow indoors or the same with quotes around it. This is a good Google query
what herbs are easiest to grow on a windowsill both without and with quotes.
http://www.richters.com is an excellent garden site too. Another site is http://www.guide-to-houseplants.com/indoor-herb-gardens.html