Hi Breck:
All the above is good advice indeed. One of my side tasks for the company I work for is our website. I do the content and work with our IT guys on the database, .php and other stuff. Because of our size, we deployed a server-side ordering system tied into our inventory and blah blah blah, so I've had to grapple with some of the issues.
I'm not going to make a specific recommendation on a provider but thought you might want to consider a few things:
As Robo said, the store part is quite a bit different and you want to consider how you plan to accept payments. There are several turnkey solutions that you can use and PayPal is a good one to consider (not to contradict Robo, but I've personally had great experience with PayPal). Set up an account to take payments and you can link off of your website through their service and they process it for you (Doug Thompson, D-Way and others use PayPal and that's how I pay them). Still, a Square reader will definitely work and you might want to just take orders over the phone and that will eliminate the cost of an ecommerce site.
Knowing how you want to take payments is one part of the puzzle. Also, you have to consider how many items you may wish to sell at a time. Sites like SquareSpace an GoDaddy have tiered pricing that allows you to price it more to your needs. I register domains through GoDaddy and they have a good service.
SquareSpace is also an excellent way to go because they have a drag and drop template system that is pretty intuitive. But they're not the only one so, as Bill says, you may wish to Google for others. There are Web.com, Weebly, Shopify and others out there. I would also look for reviews on the sites to get others' opinions.
A big question for you is, how much personal time do you want to spend tweaking a site, developing content, and so on? Back in the day, I thrived on that stuff but don't really want to be bothered with it anymore. If you go with a more or less turnkey site provider, then you spend less time on the site and more time making product. But the trade off will be the monthly cost.
Still, the costs are pretty modest for a website. I'll bet you can set up a site and prepay a year for the cost of a really nice gouge 🙂
Just my .02 (and probably worth less than that)