the first contact to you as a trainer is often an email. It is nothing but a starting point for a conversation. In your subsequent phone call you can ask about how the person heard about you. Most personal training is word-of-mouth.
What I often do it to check what I can find out about the person through available online searches such as Facebook.
If you are asked to go to a person’s home, you should first meet in a public space as Natalie suggest. If it is a serious offer,the person should not feel offended by your precautions.
Unfortunately there are several scams going on lately where you receive an unsolicited email asking about personal training. They usually ask if you take credit cards as payment and don’t provide much more information. Hopefully this is not what you are facing. Try asking more questions without giving away any personal information to determine if it is real and don’t give out any bank information.
If it seems legit, I would do the initial consultation in a public space like a coffee shop. It will make both you and the client feel more comfortable.