I want to start running but I'm afraid I'll have a heart attack?

I'm an 18 year old female. 5'4 about 138 pounds. I'm not in horrible shape but I'm also not in the best of shape. I'd like to start either running or jogging a mile a day. I started researching running/jogging to find out about how to start, build endurance, and how to breathe ect. I've come across many articles and people talking in forums about how many people have heart attacks and sudden cardiac death from running. This has me a bit scared to even start. Which is the safer route, running or jogging? How likely is it to have a heart attack? And what are heart attacks/sudden cardiac death while running/jogging caused by?