Take a SMALL deposit upfront (the actualy - not marked-up cost - of the materials. That way if they skip out on you at least you didn't lose anyting. Second, you won't give them back their car until they pay, so you always have their vehicle as collateral.

The point at which you buy materials will depend on how long the lead time is before you get them, and how quickly you're guaranteeing the service. In this day and age, the faster the better. How long will it take you to paint the vehicle?

You should schedule their appointments before they pay. You can start with a free "consultation" where they bring their car in, you walk them through the process, and explain to them how its going to work.

I would have the option to accept deposits online, but anything outside of that, I would not.

In person, you need to be able to accept cash AND credit...especially credit.

My suggestion is to have a process like this:
1) customer calls asking for a paint. Likes what you say, agrees to use your service
2) Collect the deposit
3) Go get the materials
4) Schedule a time for them to drop-off their vehicle AFTER you've purchased the materials so there's less downtime
5) Paint the vehicle
6) Customer picks up the vehicle and pays

I'm more than happy to speak with you on this further. Feel free to schedule a follow-up call and I can walk you through this step-by-step: https://clarity.fm/taylormitcham