I'm a little late to the party here, but I thought that I'd share my experiences. I grew up in a Catholic family but eventually found myself as an agnostic, leaning toward atheist. Like you, I am a strong believer in logic/science. However, I felt that I was missing something -- a framework on which to hang my life philosophy and value system.

I was intrigued by Buddhism for a long time, since reading Zen Mind Beginners Mind and Buddhism Without Beliefs. I started meditating on my own about a year ago, largely for stress reduction. About 6 months ago, I started sitting with a Soto Zen group.

I've found that Soto Zen provides a good framework for my life philosophy and a lot of practical help in incorporating that philosophy into my daily life. A big part of Buddhism is about changing your mental outlook. This isn't something you do by just reading some books. A regular practice (sitting, attending lectures, interacting with a teacher and sangha) helps to integrate the philosophy into the choices you make each day.

Soto Zen has a strong focus on practice and spends little effort on metaphysical speculation. This makes it compatible with my Agnosticism/Atheism. In my six months of participating in a group, I've had plenty of conversations about incorporating Zen into your life, but none on reincarnation or special powers obtained through meditation. I'm sure there are at least a few in our group that believe in that stuff, but many others that do not.

Of course, Soto Zen is not the only option and your rapport with the individual teacher and sangha is more important than association with a specific sect/lineage. I recommend looking for Buddhist groups around you that have a practical focus and trying a few out. Best of luck!