WooCommerce can sell more than physical goods.
SIMPLE SERVICES
Create the product and mark it Virtual, which removes shipping fields and shipping charges.
Suitable for consultations, one-off services, repairs, and anything where scheduling happens outside the shop.
TAKING THE DETAILS YOU NEED
Add custom fields to the product or checkout so customers supply what you need: a date preference, a description of the work, a reference number.
Several plugins add product-level fields without code.
BOOKINGS AND APPOINTMENTS
For genuine scheduling, with availability, time slots and calendar management, you need a bookings extension. WooCommerce alone does not do this.
Choose one that is actively maintained, and test it thoroughly before launch. Bookings plugins are among the most complex extensions available.
DEPOSITS AND PART PAYMENT
Possible with an extension. Consider whether you need it before building the shop around it.
PRACTICAL ADVICE
For a small number of services, taking payment through WooCommerce and arranging scheduling by phone is often simpler and more reliable than a bookings system.