My oldest also developed fears around that age, and even PBS shows and Dr. Suess books had frightening elements. He was also particularly concerned with our house burning down or being damaged in a storm, but there were many things that concerned him. Fortunately, this never spilled over too dramatically into major anxiety or major risk-aversion.
What we did was to discuss his fears, talk about why that wasn't a problem or wouldn't happen, and let him know unequivocally that we were careful about his safety. If your son responds positively to books, he'll likely be very open to your discussion about any fears that crop up. For example, we pushed against our walls to show how strong they were against a storm. We talked about what lightning was and showed that it didn't scare us.
As for trying new things, being a good model is important. By trying new things yourself and enjoying them, your child will see the benefits and very likely want to have a go himself. Also, if you have problems with anxiety, kids will pick that up very quickly, so it's a good idea to address that as well. Anxiety isn't a problem in our house, but I've seen this happen in families we know.
Going back to books and media, we just let him pick books and shows he was comfortable with. The period of anxiety over books was fortunately quite short (talking about how everything will work out helped, even if it did ruin the story), and now he at 6 can read books without fears, even if the movie equivalent is too scary (from Peter Pan to the Hobbit).
I hope this helps. Our boy will always be cautious, but he's never been limited by fear or missed out on anything major, except perhaps some slides he decided were too fast.
