I store my cilantro in a cup of water in the fridge, with the produce bag it came home in loosely wrapped over top. It lasts very well for over a week this way). Parsley would work well this way also.
Basil is tricky - it doesn't seem to do as well in the cup-of-water, and the more you handle it/expose it to air, the more quickly it droops and goes brown. So, I just leave it in the bag it comes in, and handle it carefully, and use it up as quick as I can (usually can get up to 5 days out of it before it's gone all limp and yuk).
The freezing trick given below is handy, but of course the reconstituted herbs will only be suitable for cooking, and not as a fresh garnish or topping.
Goal 1 - break 200 (46 pounds lost)**DONE**
Goal 2 - leave obesity behind (BMI 29.9, at 185#) **DONE**
Goal 3 - BMI = Normal (154# or less)
| current weight: 174.0