You'll find lots of hosts that offer tons of space, and space is good, but not always the most important thing. Look for a host that offers lots of different kinds of scripts and other technologies. If you' re using Front Page, be sure to ask if they support the Front Page extensions. You might want RealAudio or RealVideo. You may want your host to support databases, or server side includes.
Some hosts even offer e-commerce that's extremely easy to set up.
If you're a website designer, you might want to ask if you can sell space on your account to clients. Support With all those technologies, you're bound to be a little confused about how to use them all. Make sure your new host will be there to help you and answer all your questions. In my case, I had to get a free web email account, a la Hotmail, to be able to contact my host. Clearly, there's a lot to consider when choosing a host.