The credit checks are not overly difficult as it uses an API service, which basically means you your website sends details to the credit agency and you obtain a score.
You would need an account with a provider that offers this.
A couple are
The Experian Connect API allows you to embed credit check functionality in your websites and mobile apps.
www.experian.com
www.creditsafe.com
The listings of cars are simple enough with pretty much any ecommerce style platform. I currently manage one for a client, this runs on WordPress with some bespoke software that hooks into a system I wrote for them to control stock. We started with WordPress as it was a quick and simple way to get up and running, the longer term plan is to migrate this to a 100% custom solution as the online catalogue increases.
I would recommend planning this properly with a business plan and some solid advice, as while these types of project don't need to cost a lot of money, the biggest expenses are peoples time. The more you can plan and have a good understanding of costs the quicker these things can be developed.
My best advice is use the MVP method, Minimum Viable Product, i.e. build something that works, don't do more than that, prove the concept, even if it means you are doing a lot of backend admin. Once the concept works/is profitable, then invest in the pain points.
