Are requests usually sent with a message to email them back at their email address for more details?

I received a request from a potential client who just joined today. In addition to the brief dog and appointment request he asked to have the response sent to the email address provided. I followed up to inquire about a meet and greet through my website and the email. My question is: Is it common for potential clients to request messaging through emails or should I stick to the just the website?