Sesame, coconut, mustard, almond. In Ayurvedic practice the oil is not a lubricant — it is part of the treatment, chosen for the body in front of you.
Warming and cooling
Sesame warms and grounds; coconut cools. A therapist who picks by season and constitution rather than habit gets noticeably better results.
Temperature and quantity
Oil should be warmed to just above skin temperature. Too little and the hand drags; too much and the hand loses contact with the tissue underneath.
Storage
Buy small quantities, keep them dark and cool, and never top up an old bottle with fresh oil.