The best you can do is:
1. have the credit report run
2. ask for job verfication and/or job reference letter
3. if they are current tenants elsewhere, ask for a reference letter from the current landlord (and, of course proof that they paid rent on time)
You can refuse to allow pets, if that is a concern.
Remember, you will have an amount for security should you need to make repairs when they vacate the premises.
"Responsible" and "caring" are too subjective to quantify, and with Fair Housing laws, I'd be very careful in judging or rejecting anyone simply based on how they "look"!