How pressing is the need for your site? If you don’t need it until, say, next year, do it yourself. Keep your site local (read: on your HD) or “hidden” (just don’t make it your index.html on your host) and tweak it until it’s just right, or have dopers, or whomever, focus group it for you.
As far as hosts and stuff go, if you’re not really putting a marketing “push” behind it, you can get hosting for about $25/year without having to pay extra for bandwidth and whatnot.
Sometimes site owners use templates that have been designed for diary sites, like diaryland templates and just insert their own links and content. It’s an easy way to do it, it seems.
I meant to addition that it just makes making links easy and there are normally some very plain, uncomplicated and tabular designs out there so it doesn’t have to be flowers and bunnies in fields!
My website http://www.geocities.com/louis33772/ uses the basic design of the lawer’s site and I did it without ever seeing the one referenced. With some minor changes, the code would work for yours. If you like it, take it. As someone said, this basic design is common. One note of possible interest is that I used CSS (Cascading Style Sheet), which allows more control over formating. The entire mess is done with Notepad.
Thought I’d drop in again and mention one more thing - you can probably come up with a better design than the one you linked to.
IMHO, if you’re not looking for something fancy, just have a simple, vertical page - kind of like a printed page - with your links at the top. This way your navigation is less obtrusive/takes up less real estate, no less functional (though you may want to repeat your nav row at the bottom of the page if there’s a lot of content stretching the page vertically), and, IMHO, looks more elegant.
What you should do before you write a line of code, is draw out your website using photoshop, or just a good ol’ piece of paper. (If you use Photoshop, you can then use it, or its sister app, ImageReady to slice the graphics out, effectively saving you a step.) This can save you a lot of time, especially if you’re indecisive. 
I’ve disabled my link above because, well, it’s just too embarrassing. My point was to show that even a dummy like me can throw together some sort of website very quickly, using borrowed code. I strongly recommend the OP’s doing it all himself, if there’s time. Who knows, you might get to liking it.
The site you linked to actually does look like some kind of editor code - probably Dreamweaver. The code isn’t as simple as it seems, though I didn’t actually look at the CSS pages to see what they used them for. But, for a site like that, you should be able to look at an HTML for Dummies book and get the exact same thing in a matter of hours.
I certainly wouldn’t pay someone 50$ per page plus 10$ for additional pages if you want it done for your business. The least I charge is 50$ per hour, and very rarely does the first page take under 3 hours, when the art and everything is included.
Your best bet would be to just take the design you like - get a book on HTML to learn how to make it work, then go online to a few free image sites that will let you use their background images. There’s quite a few sites out there that you can get backgrounds and tiles for websites and google should help you find any you need.
Also, host it at a local ISP or somewhere that isn’t Geocities. Having popup ads or advertising bars on a business website looks bad. It’d be similar to handing pizza flyers with your business card.
If you have any questions on the HTML, though, I’m sure there are plenty of us who can help you with it.
John