Myth: "I found a spider I'd never seen before. Since I can't tell what kind it is, it must be new to the area and probably dangerous to my children."
Fact: I hear this, or something like it, so very often, and it makes so very little sense! A person who normally pays little attention to spiders may have consciously noticed fewer than ten species. Any temperate-zone region is likely home to several hundred species of spider. So any given specimen stands a favorable chance of being new to you, without being new to the area!
Again, spider identification is a highly technical skill, requiring years of concentrated study to learn. And even skilled arachnologists find it very difficult to identify spider species without the aid of a microscope. So if you can't identify your specimen, that's no cause for surprise.
And again, the number of spiders that pose even a mild hazard to humans is vanishingly small (perhaps 1/20 of 1% of all species) and, unsurprisingly, those few species are far more widely publicized than the harmless majority. So that specimen you found that is unfamiliar to you is therefore almost certainly nothing to worry about!