I did some research on GA safety myself to try and convince myself that it was safe. Here's what I found:
Flipping the NTSB's 1.3 deaths per 100,000 hours number gives approximately 1 death per 74,000 hours of general aviation flying.
As far as interpreting what this means, here are some thoughts:
If a student decided to get his PPL license and spent 50 hours doing it, he'd have a 50/74,000 = approximately 1 in 1,500 chance of being killed during training (with the caveat that this is the "average" pilot in the "average" airplane. In fact, flight training has a better safety record than GA as a whole).
The death rate for automobiles is given as 1 per 1.4 MILLION hours. It follows that an hour spent in an airplane is 19 time more likely to kill you than an hour in a car.
On the other hand, if you assume that the "average" auto speed is 35mph and that the average GA airplane speed might be 3 times as much, you could say GA is "only" 6 times as fatal on a per mile basis. Is this safe? It depends on how you feel about accepting a greater risk than you would riding in a car.
Good luck trying to find safety statistics for individual airplane make/models (they seem to exist only for airliners). I tried everywhere and and only came up with certain well-known airplanes (e.g. the 172) being a little safer than the average. I went with an FBO that has been in business for a long time and therefore has a history that can be researched (I only found 2 minor accidents associated with the FBO, neither recent) and (hopefully) a reputation to maintain. And there's always the "smell" test. During an intro flight at another company, I constantly smelled exhaust during the flight and afterwards I felt nauseous and dizzy. When added to the visibly shabby condition of the airplane, I decided to take this as an indication of poor maintenance and that I wasn't going to chance it on this particular outfit. If you see something that gives you doubts, why not go elsewhere?
Keep in mind that the statistics for GA are only approximate and encompass all pilots, no matter how careless or careful, all types of airplanes, no matter how airworthy/unairworthy, and all types of flight (some, like GA night IFR, are statistically much more accident prone than others).
What I get out of the statistics is a fairly sober perspective on GA flying. It reminds me not to screw around when it comes to weather, poorly maintain airplanes, drinking and flying, etc. I love to fly and decided that even though GA flying isn't as safe as I'd like it to be, if I'm careful and work to meet the requirements of piloting safely, I can probably have a long flying career. But I do this accepting that there is a certain element of risk involved.
When people ask me if it's 'safe' I'd rather just give them the information because it's up to them to decide whether it's worth it or not.