Best place to start investigating flying:
http://www.aopa.org/
For the private pilot license you need a least a 3rd class faa medical that you get from designated examiners. You need to be in good health with no cardiac issues or other issues otherwise you will need to get a special issuance. Some people can't pass the requirements and aren't given a medical. Plus the obvious training, estimated costs can be found on the AOPA website.
The light sport license restricts you to a light aircraft and VFR only but only requires you to self certify to fly IF you haven't been denied a medical by the FAA.
As lake pilot said, flying is as safe as you make it. There is more risk to flying than driving, but a big part of being a good pilot is managing and minimizing those risks.
I used to fly and hope to get back into it some day, we'll see. Good luck.