The best way to have always fresh herbs handy is to chop them and place in a jar in the freezer.
I do that with dill, parsley, celery leaves, the whole mint leaves and thyme without stems.

Except for the herbs I freeze also chopped spring onions, green peppers and other vegetables that I know I won’t eat within the week. I use them later when frying eggs in the morning.

One of the herbs that I wouldn’t recommend freezing is coriander / cilantro… it won’t taste the same, it’s taste will not be as rich as fresh one.