Well, the cost of a website is a complicated figure.
What are you planning on doing on the website? Will it require any server parsed langagues (php, asp.net, perl, etc)? Will you require a database (MySQL, SQL Server 2000, etc)? How much bandwith will you use (10gb/month, 50gb/month, 100gb/month, 500gb/month, etc)? Do you want a top level domain (.com, .net, .org, .nu, .tv, etc)?
What you basically need is to own a domain, and to pay for web hosting. The price of a domain should be around $10 a year, I use
NameCheap to register my domain (which is $8.88 a year). Depending how you answer the above questions, the hosting price will vary. A basic web hosting service will run about $5 to even $150 a month, the more features you need the more money it will cost you. The web hosting service that I'm reccomending to most people right now is from a company named
1&1 Internet, they have a nice package running at $4.99 a month; and it even includes the domain registration (which will save you the $10 a year).
Now, the unclear part of your question is if you want the actual pages of your website to be created by a company, or you want to create it yourself.