Google Forms is great and free. Google Calendar is great and free too. Our work is sync the Calendar with "drop-down" field of Forms. You can set up the Appointment Scheduling System for your business in 5 minutes. It just cost $1/1000 bookings.
For this add-on to work, your form must include a customer's email field. And this step is for you to enter where that email field is. The add-on will add users to the event of their choice and send them invitations to emails retrieved from this setup step.