Open-ended questions are very important. Try to get to know your tenant while also understanding financial situations. You need to know income, more about their at job, credit score, etc. You always want to know background and criminal history (hopefully none).
Call the previous landlord. Ask if they were ever late on rent, how they left the condition of their home, any damages, and IF YOU WOULD RENT TO THEM AGAIN. If they say no, that is a huge red flag.
For work, verify they work there and their income. Make sure you see what their management thinks of their character. Are they a problem at work?
The goal of all of this is to make sure they are financially able to rent your home and second if you WANT them to. Will they be responsible, neat and tidy? Or a nuisance, disrespectful and messy.
Use your best judgement. If you have a valid reason to not rent to them and you are not comfortable, don't.