I suggest, instead of saying No this, No that, etc. try to engage them in a real conversation. Things I always ask: Is there a special occasion you're celebrating, or is this a much needed family vacation? How many people are in your group? Ages? That type of thing. You'll learn to trust your instincts after a bit.
This will help you decide if they are suitable for your home.( When I feel our home won't work for them I often direct them to other sites that may be more suitable)
I always do 2 things before I respond, but I only have one home, so I can take 10 minutes to do this:
1) I google their email address ( you'd be amazed what you can find out if they are on Facebook, etc.)
2) I goggle their phone number to see where they live (generically). This helps me know where they are, and how far they are traveling to stay at our home.
I'm sure others will have more input.
I do the same as Debj -msdebj...it's very interesting (good and questionable) what Googling reveals.
But, if you want to hear more about the topic of "screening", just go to the top of this page here in the Community, and use the Search For Answsers field...just type in, for example, the words, screening guests. All of the previous posts contributed by Owners will appear. And, you can use that Search For Answers funtion to find all topics, at your leasure....just type in a word or phrase that relates to your question.
And, by all means, you can always just contnue to ask here.