I used to rent the spare room to mature students when my DC were little. I never fully trusted references, though, as they can be faked, and I was bringing these strangers into my house with my DC.
So, as well as a reference and meeting them, I also checked them out online to see what I could find out about them. People might say this is an invasion of privacy, but it's really not - social media is public, and you're going to live with them. Better you find out before you offer them a place if you're not going to be compatible.
I weeded out two unsuitable lodgers on this basis - both sounded lovely in person. One was racist, and the other was just a very different person from me, and not in a compatible way.
Remember, you're not only looking for someone trustworthy, but also someone who you can get on with, in your own home. Don't let yourself be talked into moving anyone in if you're not 100% sure about them.
We found renting to mature students was great as they were there for a reason, and moved on after a while, so it didn't matter if we didn't get on brilliantly, as it was only for a finite time, we didn't have to think about asking them to leave.