You have several options, some are better than others.

The basic premise is something called a "captive portal" which is the part that redirects a user's initial web request to the page where they pay. I bring it up b/c this is the trickiest part...

On the router side, most of these don't require replacing the firmware. They work basically like a proxy server that sits b/t the access point and the wan connection.

From this list, I've tried a few.

I had problems setting up WiFi dog, but it showed a lot of promise.

ChiliSpot is a classic example of one that works as a proxy...pretty solid but again not too easy to deploy.

NoCatAuth is the most popular one out there... it has 2 parts...a server (for the authentication) and router firmware (that works with DDwrt)... probably your best option.

I haven't tried PacketFense yet, but I love that it uses ARP Poisoning rather than IP filtering...slick and somewhat more secure.

Personally, I use PFsense for any router that I build. It includes a captive portal that can be modified to work with a billing system....if you need a flexable router/firewall platform its your best option, but its not the best suited towards billing...

Good luck - let us know which route you take