To operate a WWW site you require
There are many commercial, shareware and freeware web servers available. They run on a variety of platforms from Windows 3.1, Windows NT, UNIX boxes, OS/2 etc...
The number of hits that it takes daily (number of accesses to the web site) and the number of concurrent users (users connected to the web site simultaneously) will determine your web site requirements. For example the shareware HTTPD server for Windows 3.1 will handle 16 simultaneous connections slowly with much complaining. This is not a slight on the HTTPD server, as it's very easily setup and quite robost. It is operating under an operating system that is not designed for this type of operation.
A commercial Windows NT or UNIX platform may allow up to hundreds of simultaneous users without complaining. Naturally, the cost will be proportional to the performance.
The speed of the Internet connection will play a big role in how fast data is transferred. The term used in networking is called bandwidth (BW). The larger the bandwidth, which is measured in bits per second (bps), the faster the files will transfer. A typical modem transfers data at a rate of 14,400 bps. This is quite adequate for a single user transferring graphics. A text based browser will scream along quite well at 2400 bps but die if any large files such as graphics are downloaded (takes a very long time).
The more users that you have accessing your web site, the slower the response will be. Low-end web sites can get away with a 56Kbps line (56,000 bps). The users don't actually use all of the bandwidth at the same time. People tend to download a web page, read it , think about it for awhile and then download another web page. The result is bursty traffic where many more users can access the site than initially expected.
Is there a rule for selecting the speed of your Internet connection? I don't know but I would suggest that you speak with Web sites currently running to see what their hit ratio is and what bandwidth they have.
Something that is indispensable is someone who knows the system inside out. This could be a person on site or a contractor who is available 24 hours a day. If the success of your program depends on the Web site operating reliably than you absolutely need someone that can be counted on.