When picking an oil to use for a massage, you don't have to go out and buy the fancy bottled stuff that masseuses and masseurs use. You likely already have oils in your kitchen that work just as well, including olive oil, almond oil and my personal favorite, virgin coconut oil.
When I occasionally splurge and treat myself to a massage session, I always ask the masseuse to please use the virgin coconut oil that I bring with me rather than her own oils. Nothing against the stuff she uses, but I prefer virgin coconut oil because of all of its beneficial properties, and it's a perfect massage oil, as just a small amount spreads easily across the skin without feeling tacky and hard to move.
Virgin coconut oil also provides a perfect base oil for any other essential oils I want to mix in for a more pleasant and aromatic experience. Currently I like to mix about 20 drops of chamomile essential oil into 3 oz. of virgin coconut oil and use that as a massage oil. I always end up smelling faintly like chamomile tea after the session, but not so much that it's overwhelming, and the combination of chamomile essential oil and virgin coconut oil really helps make the massage experience quite soothing and relaxing.
If you prefer using a different essential oil, go for it. Lavender essential oil is also known for its calming properties, and many people enjoy using that during massages. Just remember to always dilute essential oils with a carrier oil before using them, as they can be quite potent on their own, and you wouldn't want to trigger an allergic reaction.
Of course, if virgin coconut oil is not your thing, pick another base oil that you like. Many people enjoy using olive oil, although I personally find it bit too tacky and difficult to use as a massage oil. But almond oil and jojoba oil are also good alternatives.
An important thing to remember: if you have sensitive skin, remember to test any massage oils you plan to use on a small patch of your own skin before using it for a full body massage. Simply rub some into the inside of your wrist, or the inside of your elbow, and leave it for a few hours to see if it triggers a reaction such as itching, rashes, or hives. If it doesn't, I'd say you're good to go.