Welcome to the world of BHPH which is very different from being a private seller, in order to be profitable you have to avoid common mistakes. There are about 10 ways to be profitable and 1,000 ways to go broke. You're right, people will expect to put down close to nothing compared to what your cost on the car is.
Example: Your cost on a Honda Civic might be $4,500 after reconditioning. Along comes a client offering you 1k down which leaves you $3,500 short (also known as CIV - Cash In Vehicle). This is why in your business plan you have to know what your maximum CIV is for any sale. If you ignore your CIV and just start financing everyone with low down payments then it is very likely that you will run out of money to buy more cars which eventually can cause a dealer to close down.
My suggestion is sell cash and only finance clients whose down payments come close to your Investment. Keep in mind you can deffer the other part of the down payment for the first month or so in order to get the down you need to restock inventory. Make sure to qualify people, the last thing you need is to take a $500 dollar down payment but then spend $1,000 on getting your vehicle back after they've taken out parts.
I hope this helped.