You will never, ever get every spider out of your house. They’re as unstoppable as dust and taxes. But you can reduce their population to a manageable level—one where you only see one or two a month, and they’re polite enough to stay on the ceiling.
So seal the cracks, spray the mint, and remember: that spider is just trying to eat the real pests. Unless it’s in your bed. Then you have my full permission to scream, trap it in a cup, and release it into the backyard of someone you don’t like.