Photos are big part of your website, and especially because of the nature of your business. Pet owners are pet parents, and they want (need!) to feel secure with the person or company they engage to care for their babies.
Pet owners want to feel happy and secure, and you will gain more interest in your site by catering to that.
You should therefore place an image of a human with an animal near the top of your home page. This is the first place a prospective client lands, and that photo will help set the mood of your site.
The photo can be of you or a staff member (but not a stock photo), and should show the person looking either at the camera, or at a pet. The person should be dressed appropriately, and should look competent and warm. You basically want this photo to be the one that best represents your business.
This will also help with your Meet and Greet sessions, because you can tell your new prospective clients to expect the person in the photo on the home page of your site.
This image is from the Auntie Em’s Pet Sitting and Dog Walking site. The owner is seen front and center, welcoming you to the site and showing that she is warm, friendly, and competent. She has two dogs with her, and everyone seems comfortable. The photo is nice but not overly posed. Nothing about it screams “professional!” With reference to that, photos don’t have to be taken by a professional photographer; they can be taken with mobile phones, because most searches are done on mobile these days anyway.
Auntie Em’s setup is what you want to work toward: a photo that makes the viewer feel good about you. And placing that photo on your home page is the best way to welcome prospective clients and set the tone of your site.