Just one thing to add: look at Google Sites (which is part of your Google Apps service) as a method of creating and publishing your website. If you find it acceptable, then you can also cancel your web hosting (after you've set up your site on Google Apps and are happy with it!!). As noted by others, you will still need to have your domain name registered with someone and use their name servers.
Pros of Google Sites:
1. Its free (in as much as its included in your Google Apps licence (which itself is free unless you're using the Google Apps for Business version (which incidentally I always recommend for businesses due to the 99.9% uptime guarantee, phone support and no-ads)))
2. Its relatively easy to create a website there (What You See Is What You Get rather than needing programming skills)
3. You can easily do fancy things like incorporating a Google Apps calendar, have surveys and forms.
4. Because its easy to use, any staff can update the website frequently to keep it fresh with useful, topical info.
Cons of Google Sites:
1. Its not easily highly customisable in terms of design. That's the other side of the coin to it being easy to use. We built our own website at www.cloudlogic.com
on Google Sites to show what can be done and are satisfied with it.