This answer will depend on where you live. I live in the Midwest so anything that cannot grow in zone 5b will not make it through the winter. So plants not for this location I grow as an annual, knowing it will die and have to be replaced. Some plants will never be successful here because the growing season is too short. That being said, here are my recommendations that should work in many areas.

Here are my three easiest herbs to grow

1. Thyme - pretty, great in pots and in the ground, drought tolerant and tasty and easy to dry.
2. Basil - although it needs, heat and sun and must be pinched back regularly to give you lots of leaves to harvest, it grows quickly from seed and there are lots of varieties to choose from. I like the smaller leaves of lemon basil and the colorful leaves of purple basil.
3. Dill - a plant that you can use the leaves (dill weed) and the seed to cook with. It grows easily from seed and works best if you drop seed every two weeks to give you a constant crop. It is not picky about soil and sun light, but all herbs love sun and drained soil.

Here are the 3 trickiest to grow

1. Rosemary - likes rich soil and moisture but does not like to have wet feet or conditions without enough humidity. Too much rain or sitting in a saucer with water constantly will result in plant failure. It is a slow grower and cannot winter over in many places and if you bring it inside if the area is too dry where you place it it will die (almost instantly)
2. Mint - although it is easy to grow, it requires maintenance and diligence to keep it from spreading or taking over, so if you are not up for that, don’t grow it.
3. Parsley - this herb does not grow well from seed and is a biennial, so it will winter over, but the second year it will produce a flower shaft and seeds. However most of the seed will be not viable or with a low germination rate, so I just grow from a plant and remove it at the end of the year. Harvesting the plant and drying can also be a challenge. If the leaves turn brown the taste is lost, you can lose up to 50% of what you are trying to dry.