if your host provides mySQL, then it's more likely they will also support PHP instead of ASP (--> practically only runs on Windows Professional or Windows Server, and such hosting is usualy more expensinve and would come with MsServer as a database). ASP (=classical ASP and not ASP.NET) would not be your best backendoption. Its not a realy longtermsollution + you'll have a harder time finding 'mySQL and ASP wise' programmers. (I'm one, but i don't have time now).
I need a website on which a customer comes in, puts its information and registers, then logs into hes account and looks at the details, and can pay from there, and log out.
Thefirst part of your request isn't a problem. It's more a less something every experienced programmer will already have somewhere lying around (or else they should only riun a search a www.hotscripts.com for a useradministration system)
But then the 'paying' enters the frame. This means that security should be made a bit tighter + that you'd need to get an account on some paymentservice or so + that it needs to be integrated. Not that hard, but you'll need to pick a company that will handle your payments (like PayPal or so). Writing this as a custommade service could get rather complex and expensive.
I myself would need to see the whole database in my account after logging in, to understand the needs of my customers, and whom I am dealing with.
Again, something most coders allready have or can easely find somewhere. It's basically just a small admin-section.
So it comes down to : rather standard product, that can easely be created from an e-commerce or shopping cart application (plenty of those are available for free http://www.hotscripts.com/PHP/Scripts_and_Programs/User_Management/index.html , http://www.hotscripts.com/PHP/Scripts_and_Programs/E-Commerce/index.html). Only tricky part may be the paymenthandling, but here again, there are easy to integrate services (for paypal, see http://www.hotscripts.com/PHP/Scripts_and_Programs/E-Commerce/PayPal/index.html) if you would be willing to take an account somewhere. (this comes with a small recurent cost)
a good coder should be able to create this rather quickly, unless you have specific needs that are not covered by the packages/code they start from. But you'll non the less be looking at about $1000 (a day or so fintetuning your requirements, a day or three setting it up, a day testing, some customisations/fixes after testing ...)