Everybody's "best" oil is also everybody's "worst" oil. We each have our favorites, which the next guy will tell you are terrible, cause fouling, won't clean up well, cause global warming, will make you support the Brady group, etc., etc.
General pronouncement, which at least one person will say is not true because they've never had a problem: petroleum based oils are bad because they react with bp combustion byproducts to form tar. However, they do a good job of rust prevention. Bottom line: use them if you wish but be sure to clean them out thoroughly before shooting.
Mineral oil based compounds are generally well thought of, although some don't agree: Ballistol, Butch's Bore Shine both clean and provide rust protection.
"Natural" oils: olive oil, peanut oil, crisco - all work but will turn rancid over time.
Specifically formulated compounds such as Hoppe's No. 9 Plus and T/C's Bore Butter each have their fans.
Those are just off the top of my head - I know I've missed some but I'm confident someone will fill in the blanks. This is a subject that everyone is an expert on, and I don't mean that in a derisive way.