Does anyone have any tips on keeping spiders out of the house?

I've found 6 spiders today! I killed 5 of them and caught 1. I think it's a black widow and plan on taking it to our apartment's main office tomorrow. I'm so angry! They just came and sprayed our entire apartment last month and then came and did their routine spraying last week. We have an 8.5 month old and he spends a lot of time crawling around. I've never seen spiders like this. The one I just killed was huge! At least the size of a quarter.

Help, please!!

ETA: Here's the most recent one!