Is there any payment processing that offers a sort of reassurance for buyers? What I mean by that is, for example, a customer purchases a service offered by my business from my website, the payment would then go to a neutral account instead of mine, to be held until the service is complete. If it happens to fall through then the customer can get their money back from holding bank's neutral account. Why I ask is I want to be sure that the payment will be there for my services and I won't get ripped off, also I want my customers to feel assured that their not taking a risk by paying for a service that ends up going south. Even though this is highly unlikely, I don't think that everyone else feels that way.
may not be what you're looking for but Paypal has a fairly strict buyer protection policy. Generally speaking, buyers words are trusted before sellers and at the very least funds are held and complaints investigate should one arise...this would be a great link to share with customers: Paypal Buyer Protection Policy (1st link, for some reason dp wouldn't let me post the direct link so here's the google result)
What you want is an escrow service. Attorneys can do it and there's electronic services such as escrow.com that do the same thing.
If you're looking for a payment gateway or service (web service etc), Paypal would be a good option. You can get set up to process payments etc. very quick, that would accept credit and debit card payments. I am using it and I got a lot of advantages here for payment from my clients.
I hate paypal. I would rather just use someone like secure trading where they offer 3D secure processing system.
Why not just "Authorize" the payment to make sure funds are available and then hold the settlement process until the service is complete?