Since Google Sites is possibly the most economical way to build a church website (and have all the other office and email tools you'll need), you might consider it for your church. These websites are not totally simple to use, and the content management system does not give you many options, but the sites work, and you can embed your Google documents easily. Calendar is easy, too. Not many add-ons or support, but I recommend it if you have someone willing to learn and teach using it, and it's easy enough to try out.
However, Google Sites, at least older ones, are not mobile-friendly by default. The video below will show you how to optimize for mobile. You website might not look any better, but Google will now see it as mobile-friendly. It will only take you a few seconds, so go ahead and do it. And I checked my sites out on mobile: they look decent. Menus are hidden until selected, and the blocks are automatically stacked. Not bad. In fact, I think Luthernet can officially say that we'll build your Google Site for you. Take a look at https://sites.google.com/site/brianjaegerenglish/ on a mobile device.