Do you offer online payment for any other services that you offer? If so, that's probably the easiest way to go. If not, it's probably worth looking into some of the standard online payment platforms: Square (https://squareup.com/)
and Stripe (https://stripe.com/) seem to be the two big players in this area.
I started using Stripe recently for some things and have been happy with it. As far as I know, both "play nicely" with various web platforms, including WordPress.
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