To get started using essential oils all you need is a bottle of essential oil (e.g. putting a few drops of lavender on a tissue under your pillow. As you progress you might consider some of the following:-
A book with key oils and their uses.
An oil burner to make room scenting easier.
A selection of bottles from perfume roller bottle to spray bottles for room scenting.
An electric oil burner or diffuser for nighttime use of where a candle is not suitable.
A storage box for oils (although a small cardboard box is fine too).
A selection of base oils.
A notebook to record your favourite recipes and blends.
A growing oil collection to increase the things you can treat, the smells you can enjoy and to more.