Some oils do break me out. I can't use lots of cocoa butter. It's definitely a pore-clogger for many.

Jojoba is a great one. Very similar to your skin's own oil, but lighter. Shea butter is useful for a lot of people too. Argan never breaks me out.

If you do better with lighter oils, you can get jojoba on its own cheaply at any natural store or natural health section of grocery stores. They usually sell nice stuff like vanilla absolute and lots of essential oils nearby so you can customize your own oil. Bottles of essential oils usually list ratios and the like.