In reply to chris687:
If a whois lookup on a domain name says it's available, then there are lots of Registrars that you can use to register the name.
I have 4 domains on 123-reg - a few quid each per year, but about £70 per year for a hosting package.
And all 4 sites are "hosted" on that on hosting package.
You may want lots more email addresses for your domain than a basic hosting package costs.
There will also be monthly bandwidth limits, at that price.
Also, it depends on what this company want to do with their website.
If it's just a flat, informational site, with a few pages, then the above is probably fine.
The key is to find your customer's requirement.
Do they want a Contact Management System (CMS) or a Customer Relationship Management System (CRM) ?
If so, those can be quite costly, require a different sort of hosting, and programmers to write code and set up databases.