Although sites connected via dial-up lines do exist, it's not an approach for serious business users, either on performance or availability grounds. That's enough to support a smallish site taking a few thousand hits a month, but only if you're not expecting to host any downloads. The only real drawback will be the call charges, especially if you want your server to be available 24 hours a day, unless you get an unmetered agreement, such as BT Surftime, for example, which allows you unlimited access for a fixed monthly fee. Alternatively, it ought to be possible to use ADSL, which gives an always-on Internet connection at a fixed monthly fee. Another consideration with ADSL is that some ISPs periodically disconnect the line to discourage it being used for Web hosting.
Some providers also offer burst bandwidth agreements.
These operate like bank overdrafts, where the provider allows you to exceed your normal bandwidth limits. This facility means you don't need to have expensive leased-line capacity sitting around idle when it's not needed. Or you might want to look at co-hosting agreements where you supply the server, but it's located at the ISP's premises, making the need for a high bandwidth link redundant. Then there's the important issue of security to consider. The most secure way of implementing a Web server is to disconnect it from any other systems or networks in the company.