The Web servers should have fast CPUs, a lot of memory, and high speed disk drives. Even if you are not engaging in transactions over the Internet today, you might be tomorrow. Your provider should have an option to have either SSL or PCT encryption set up on your Web site. Your provider should also make provisions for getting the sensitive information from the Web server to your office location in a secure manner. Although this seems like an obvious question, you would be amazed at how many companies have less than 6 months of experience in Internet services.
Experience does count, and is very important when selecting a Web hosting provider.
Again, this may seem like an obvious question, but actually is an important point to consider. When you are talking to a potential provider, ask some Internet questions and make sure you are happy with the answers. Also, be sure to call the technical support line. Since these are the people you will be dealing with, you should feel comfortable with them. Finally, check out the Web support pages.