The wikipedia article on near-Earth supernovae [1] suggests that Betelgeuse will be pretty safe because of its distance. But exactly how safe? What about all the delicate electronics that we've sent up to space? I suppose anything that can withstand a daily dose of solar radiation would probably be okay, but are there any specific wavelengths that could cause an issue?
That said if you had some instruments closer to the heliopause you would definitely be able to detect the shock wave at that distance. It would be faint but should be well above the noise level of other particles.
I'm not sure the Betelgeuse supernova, at a brightness around that of the full moon, would ignite fires, but I certainly wouldn't want to gaze at it with naked eyes, even at that brightness. IMHO such a light, given sufficient strength, could permanently damage the retina in your eyes.
You should know that even an impossibly tiny point source will get projected to a spot of finite size on the retina. The eye is not perfect - there is always some optical aberration. Plus, since we're talking about a star, there's also atmospheric distortion to think about.
The chances of light from Betelgeuse igniting a fire are very much zero. We're talking about light intensity about 10x lower than moonlight.