I believe the accepted answer is what your looking for, but I want to throw my comment into the ring, as I think it is important to keep things in perspective.
If you plan on building and running a blog, you can basically do it for free without much fuss, as long as your blogs requirements are straight forward.
The key is why you need a database in the first place, as a blog is primarily static content that is the same for everyone everywhere. This is where Static Site Generators come in and stuff like the JAM stack, where you compile your site and deploy the final compiled version. Now if you were planning on creating your own CMS that leverages a DB for a bunch of bells and whistles then this plan probably wont work, as you need a DB for stuff like user sign-ins, or “likes” or comments or other fancier features.
Now if you just want to run your own blog and worry less about the bells and whistles and focus on content and maintenance then keeping things simple is probably better. As such using just Firebase hosting and a static site generator would basically be a 2 line deploy (build -> deploy) be stupid fast, and basically free to run. (might have to pay for an actual domain if you want a non-firebase url)
I’d be less concerned about Firebase costs, as long as you build your DB correctly and don’t run into any of the big issues like reading the entire db for every user all the time. The only Firebase limitation I’d keep an eye out for is document size limits, which is 1mb which is pretty big for just plain text, but could be a concern depending on how you use your Firebase documents.
Otherwise Firebase is a cheap/free db along with mlab hosted mongodbs. If you need a back-end, free tier options are Heroku, Google App Engine, which are Paas offerings. DO and the other big three clouds all provide pretty cheap Iaas, but these may require much more maintenance and hand holding.
Just make sure you understand what each choice your making entails, don’t think you need to go run DO, and build everything from scratch if your goal is to just make a blog to build content.