I was asked about using Google Suite at a church recently. I sent a fairly detailed email to members of a church in New York detailing the awesome applications and limitations of using Google at the church. If your church is considering a switch to Google, this is probably a decent article for you to figure out if it's right for you (it is), and which parts might make more sense to use than others.
My last church in Kansas used Google quite a bit, but that church made the mistake (school side) of implementing Google Classroom too quickly for the teachers and students. That's the biggest issue: people not used to it will feel like it's too much unless they are given some guidance and time.
My current church used gmail tied (forwarded from church email) and not much more. Then I showed the administration how easy it is to add newsletters (scroll to bottom) and documents to the websites. Also at Faith. And Google photo "albums," too.
If you're also deciding on Google Sites as a website, that's a bit more complicated. It's not good, but it's not terrible. Probably better than an edline site on many school district pages. My 3rd grade son made this site with no guidance from me. But it may not be a good fit...see this article I wrote -- check out Shepherd of the Coast, Beautiful Savior Sarasota, and Faith Viera.
The new Google sites works fine for ALL static content and embedding Google stuff, like docs and calendars. Blogger can work well just for lists of articles. Combined, those would work for a church, but they are separate Google products.
I know you have a small church looking to save money. Google Suite can be very useful, and I know from evaluating sites that many LCMS churches use the calendar, gmail, and even Docs; fewer use Sites--none effectively. That said, it's better than your current blank page links (from LCMS and other sources) and Facebook-only scenario. If my kid can make a decent landing page with it, then it's at least an option. It's what your time is worth, as much as anything, as any new system (Suite, Calendar, Sites) takes some time to learn.
I build websites with Joomla, which is like Wordpress. I charge from $500 on up, and it's a good system because it allows some blog/news sections and some static pages, looks a bit more professional than free options, and it's set up easy to edit the articles. Just better/more options. But I know it might not be right for you. Mostly, whether church or business, I encourage people to have something up and to update the content.
Here's my book on church website design. If you're ever in Jacksonville, stop by Grace and I'll hand you a copy.
Best of luck in your search for a better way to do things.