Use Wordpress if you're familiar with Office tools like Word. Watch some videos on Youtube to learn about it.
Advantage: you own the domain.
If you're not, there are plenty of drag-and-drop builders available out there.
Disadvantage: you don't own the domain; it's a subdomain of the host eg. yoursite.wix.com
I just built a new website for my business using WordPress and a custom theme (the7). It is a drag and drop with excellent tutorials. While I had a couple of things that really tripped me up, I reached out to the customer service for the theme and was able to figure out how to correct what wasn't working as I thought it should. I believe the theme came with six months of customer support from the theme developer, with the option to buy an additional six months for a small fee.
To find the themes, I used Theme Forrest. It is essentially a catalog for custom WordPress themes. Each gives you the ability to look at demos of sites built using those themes, examples of specific page types and information on how to build the page (is it a drop/drag, requires coding, etc).
To build a site from scratch, you would need technical knowledge. No getting around that.
These days, web design is far more sophisticated than it was in 1998. Lots of extra bells and whistles are expected by consumers. So it's unwise, expensive, and laborious to begin from scratch in most cases.
Even professional web designers typically begin with a functional template, which they alter to meet the needs of a given project.
Amy Austin's recommendation is a good one. Browse WordPress themes at a site like ThemeForest.net. Pick one you like. Usually that's around $50. If you don't want to set it up yourself, you can hire someone to do it for you at a site like Freelancer.com. There lots of people will bid for the job, and you can choose the designer based on skill and price.
Visual layout can be changed. But if you need features and functionality not found in any of those WordPress themes, then you may need to use an underlying platform other than WordPress. 5% chance of that.
Why are you looking to do it yourself? if is because of the price restriction that most businesses get from web designers, I would like to offer you our services at www.Unthink.me - we offer web design on monthly payments.
Now, to answer your question there are many places where depending on your need of the website meaning that if you are not looking to complete online sales or sell goods, you might be ok with an information only website that may look outdated or all text just to prove your existence - then you can use pretty much a website building tool that most web hosting and domain providers offer. If you are going to depend on web sales you need to have a website that is not only well built on the back end and comply with search engines needs but also have items and content that speak directly to the visitors and convert them into customers.