Glitteringwhite

We are searching for the best check out flow possible: how to integrate in our shop:
we want customers to be able to book an appointment and have them pay for it upfront AND have them fill in an intake form too. So 3 things. How to set this up in the best streamlined way? We don't want to lose customers in a check out proces that confuses them. Thanks for your suggestions!
(We already use scheduling/acuity)

This sounds like a perfect situation to use Squarespace Scheduling (previously Acuity). 
It is an online appointment-booking tool built into Squarespace. Enter your availability and the services you offer, then use Scheduling to share your schedule, receive online bookings and take payments. You can optionally send reminders and follow-up emails to clients.
You can try it free for 14 days. 
 
 

Without more information about the use case, it's difficult to offer specific suggestions. To help us, please provide a working link to the page where the service is purchased as well as a link to the page where you want clients to schedule it. That will give us more context and help to explain why Squarespace's new Scheduling product doesn't meet your client's needs.