I used to invite the child and the parent over to the house for the first playdate. I would explain our rules of the house and let the girls play.
I showed the parent around our house tell them about myself and my husband.. etc. ask about them and their family.. etc.. Then if I felt comfortable, I would say. if you have things to do, you can come back in 2 hours. Here is my phone number, let me have yours.
From there, we felt comfortable with each other.
I also would get to know people at the school and so I could ask around. So and so asked my daughter over, do you know the family? Get some infor that way.. i am sure people did the same with me.
Be PRO active, so that you are inviting them over to your home first.. Then you will get an idea about them..
Overall, really most families really are so much like us, it would shock you.
We may look different, have different backgrounds, live in different types of homes, etc. But we all love our children, want them to be safe and happy and want our children to meet other good children and parents.
Our children need to learn about manners, how to be a good host, how to be a good guest, how to meet people, etc.. This is a perfect time to do this, by leading the way.
I have had many parents tell me they were always so shy until their "social children' forced them to become social! I love it. We are all just parents doing our best for the children.