This. The scientific community - in other words, millions of people working for hundreds of years, using all the reasonable means they could come up with - has so far found no trace of the supernatural. In order to go against their work, you'd need some rather heavy evidence. Do you have any?
See also Privileging the Hypothesis and Burdensome Details.
Also, you say you don't have a good reason to reject the supernatural altogether. That suggests that there are some specific supernatural things you still believe in. Be specific - exactly what are those? What makes you tempted to accept them as true?
"The supernatural" is such a broad category that asking "should I believe in the supernatural or not" is really a rather abstract question, and hard to give a definitive answer to. It's much easier to concentrate on the specifics. Take every thing you are tempted to belive in and might classify as supernatural and ask separately, "should I believe in this or not?".
I don't have any supernatural events or beings in mind, but I am tempted to say that consciousness, free will and moral absolutes are evidence that the world is made of something more than atoms. Thanks for responding.
Background
I was raised in the Churches of Christ and my family is all very serious about Christianity. About 3 years ago, I started to ask some hard questions, and the answers from other Christians were very unsatisfying. I used to believe that the Bible was, you know, inspired by a loving God, but its endorsement of genocide, the abuse of slaves, and the mistreatment of women and children really started to bother me.
I set out to study these issues as much as I could. I stayed up past midnight for weeks reading what Christians have to say, and this process triggered a real crisis of faith. What started out as a search for answers on Biblical genocide led me to places like commonsenseatheism.com. I learned that the Bible has serious credibility problems on lots of issues that no one ever told me about. Wow.
My Question
Now I'm pretty sure that the God of the Bible is man-made and Jesus of Nazareth was probably a failed prophet, but I don't have good reasons to reject the supernatural all together. I'm working through the sequences, but this process is slow. I will probably struggle with this question for months, maybe longer.
Excluding the Supernatural was interesting, but it left me wanting a more thorough explanation. Where do you think I should go from here? Should I just continue reading the sequences, and re-read them until the ideas gel? I'm coming from 30 years of Sunday School level thinking. It's not like I grew up with words like "epistemology" and "epiphenomenalism". If there is no supernatural, and I can be confident about that, I will need to re-evaluate a lot of things. My worldview is up for grabs.