Jojoba worked fine for me when I was on benzoyl peroxide but when not using it, jojoba broke me out badly. Olive oil I've heard ok things about- some do very well and some do horribly. I've heard a pretty consistent rave about grapeseed oil though and I started using it two days ago. Check the reviews it sounds fabulous. The key with any oil though is to go easy and not overboard. I learned the hard way: only use a few drops and pat or brush with clean fingertips onto cleansed skin

Jojoba oil works really well for me at the moment and I'm on 5% BP.