This might be a better solution if you're already using QGIS - there's a plugin called QGIS Cloud. It has its pros and cons:
On the pro side, it's very easy to use - if you already know how to use QGIS, there's very little else to learn (perhaps how to make map tooltips, but that's simple). You also don't need a website to display the map.
On the con side, the free allocation - 50MB - is pretty stingy. It also doesn't work well with QGIS 3 yet, so it's best to use legacy QGIS 2.18. Also, with a free account, you can't put the maps up on your website, if you have one.
Here's an example of a map I just made using QGIS Cloud:
https://qgiscloud.com/cinyc/SD_37/The tooltip is a mouseover event, so it works well with a computer. I haven't figured out how to get it to work as a popup for cell phones - yet.