Drying oils are oils which dry to a solid and elastic film when exposed for certain periods of time to air. This chemical process is known as oxidization. Drying oils are used in oil painting to bind the pigment.
Drying oils include linseed oil, tung oil, poppy seed oil and walnut oil. Non-drying oils include almond oil and olive oil and are not suitable for oil painting.
Different oils have different characteristics and drying times.
Linseed oil is one of the most commonly used oils for painting and is a great carrier of pigment. If you are just starting in oil painting then read no further - linseed oil is a great choice for your medium. It is otherwise known as flaxseed oil and is derived from seeds of the flax plant. It has a clear to yellowish color and can be used to increase the fluidity, transparency and gloss of oil paint. Linseed oil has tendancies to slightly yellow with time but has one of the highest strength films once dries, hense why it one of the most commonly used mediums for oil painting.
Poppy seed oil is a common oil used for oil painting. It has less tendancy to yellow with time than linseed oil and dries slower. However it is thought to be more britle than linseed oil, as the fat which is responsible for the yellowing of linseed oil which also provides durability.
Walnut oil can be used in oil painting and has less tendancy to yellow than linseed oil but is also less durable.
Safflower oil is dervised from safflower seeds and has similar properties to poppy seed oil, however it dries slightly faster.
Tung oil is obtained from the seeds of the tung tree. It is mostly used for woodwork and is generally not recommended for oil painting.
You do not need to test all the different types of drying oils to see which you prefer. If unsure, just use linseed oil. It is widely preferred for a reason - it is a fantastic carrier of pigment and provides a very strong film compared to the other oils. The only downside is the yellowing over time, which can be addressed with certain means.
(You might also be interested in my Painting Academy course. It goes into much more detail on the fundamentals of art.)