Tips for meditation when family has a frightening supernatural history?

When I stress (even subconsciously) I sleep poorly, tend to get migraines and my wrists begin to ache fiercely. I think meditation might be helpful in stress relief. But both my mother and grandmother have experimented with meditation in their youths with strange and scary results. They both claimed appearance of similar "evil" beings they could not explain. They say these things didn't just appear but spoke to my grandmother and physically messed with my mother. The beings left them alone after they stopped meditating altogether and have never reappeared to them. They have only recently shared their experiences with each other and now with me. Now I'll admit that I've had a small share of things that I couldn't explain, things one might call "supernatural." But I believe everything has an explanation even if I don't know what it is yet. I'd like to call myself an open-minded skeptic. So for the sake of caution, I'd like some tips on meditating.