The best oil I’ve used has been cold-pressed linseed oil. Cold-pressed oil combines with colors well, and doesn’t ‘suede’ like refined oils.
Cold-pressing refers to extracting oil from flax seeds with a mill or press and without heat or chemical processes. The resulting oil is highly acidic, which is why it combines well with pigment.
Cold-pressing is inefficient so most commercial oil–by far–is extracted with heat or chemicals.
Refining refers to cleaning the oil, regardless of the extraction method. Many consider cold-pressed oil a finished product, so the term ‘refining’ is usually (but not always) applied to non-cold pressed oil. A frequently used cleaning method is alkali-processing in which the oil is filtered and washed with alkaline water to remove impurities. Most commercial artist-grade paint is made with alkali-processed linseed oil.
Alkali-processed oil is much less acidic than the cold-pressed variety and, therefore, combines less readily with pigment.
Some artists prefer alkali-processed oil to cold-pressed oil (most have no preference), and others use some type of refined oil. There are many types of refined oil so that is a discussion for another time. As for me, I prefer to make my own medium and nothing beats cold-pressed linseed oil for that.