I've had to look around to build a new site myself recently-- just to build a basic information based site though, not a e-commerce site like you.

I heard good things about Wix, but my understanding is that if you buy from Wix or most similar platforms, you are also locked into hosting there. Since I'd already bought my domain through hostgator (2 yr package) and set up my business emails there, it didn't seem a good fit.

One option similar to Wix that did catch my eye is MotoCMS. Here's a link to their eCommerce templates:

motocms

Haven't really looked through these specfically (again, I wasn't looking to build an estore), but the aesthetic quality of their basic informational type websites is a bit better than average compared to the other template based sites I looked through and I found one I really liked.

They primarily recommend hosting with inmotion (which from what I've seen gets pretty good reviews, generally better than godaddy, 1&1, etc.) and bluehost, but you should be able to port your completed site to other host providers as long as they meet the requirements of motocms... this is actually the sticking point that prevented me from pulling the trigger... One of the requirements is the host provider use "Zend Guard Loader". Hostgator uses Zend, but not on my hosting package. I asked hostgator tech support if it would work, and they said if I could download the site and upload it into hostgator they "should" be able to make it work. I asked Motocms to confirm, and they said, "tell you what, we can just give you a coupon to get a year of free hosting at inmotion."

I've been too busy since then to follow up or do anything, so I'm still not sure how this would play out. My point of the above tldr paragraph is to let you know the only potential sticking point I found from motocms being a slam dunk, and it may or may not have been a true problem. I still don't know. Otherwise, I did the free trial with their builder and it was easy (I have no experience). So, for ballpark $200-$300, it might be worth looking into. And I think some of the basic non ecommerce websites also have an add on line item of approx $60 to add an "ecommerce plugin" whatever that specifically is.

Best of luck.