What you are asking for is ‘Internet Cafe’ or any of a dozen programs that handle authentication and management of attaching nodes to your wireless access point (and wired nodes). Your internet connection comes to one system. The wireless and internet distribution goes to your network on a second port on that system. ‘Internet Cafe’ runs on a bootable Linux CD and does not need a powerhouse system to handle 50 to 100 connections. I have not found any of the small router/gateway appliances that can run 3rd party software for your requirements.
‘Internet Cafe’ is a generic term not a product (as far as I know). There are a great many versions offered by commercial companies and through SourceForge as ‘open’ software projects. (i.e. ‘GlascowNet’)