If this is the case, you may want to contact your ISP and see if they will host your site. Dial-up connections normally are not permanent connections. In other words, the connection is live only after you have dialed up your service provider. Anyone trying to get to your site would have to wait until you make the connection. Additionally, to dial up, you tie up your phone line.
Modems are slow even when compared to other Internet connections.
A Dedicated Subscriber Line is a fairly new service. DSL can be very fast. You can also multiplex audio and data over this kind of a connection so it doesn't necessarily tie up your phone line. But to keep this affordable to most home users it is still a dial-up service. DSL will cost more money than a normal phone line connection, and the cost for the dedicated line you would want for a web server is high.