I am pretty sure the first time I used the EC2 free tier about 9 years ago, that page already said 750. I cannot vouch for anything further back. Shrug.
AWS is used to host a lot of the popular games that we all play:
https://aws.amazon.com/gametech/compute/
And to get started at little or no cost, depending on your volumes: https://aws.amazon.com/free (It is actually 750 free hours per month.)
Personally I really like the play framework for building REST APIs: https://www.playframework.com/
And this short book should get you going quickly: https://www.amazon.com/Play-Framework-Essentials-Julien-Richard-Foy-ebook/dp/B00NXWI1AI
I agree it could be a fun project to build ones own TF-IDF rankings. And the article you have linked is really good. Thanks for providing it. I was under the impression the OP just wanted something that would work. Free text searching does take some effort, so I guess the OP shall have to learn...
Something like ElasticSearch might unfortunately do the same, due to the higher frequency of the word: https://www.compose.com/articles/how-scoring-works-in-elasticsearch/
But maybe not, since ES also takes field length into account.
And yes, ES is its own database. I still think in the long...
If you go with AWS, you can also let them manage the certs (and the certs are free for the AWS provided ones), so you do not have to deal with the renewal hassles that comes with Let's Encrypt: https://docs.aws.amazon.com/acm/latest/userguide/acm-overview.html
AWS also makes it really easy to...
Why not go for AWS directly, otherwise you have to mess around with your company DNS setup, which might break other stuff:
https://www.google.com/search?q=route53+and+api+gateway
Also, you probably want to use some kind of prefix like:
dev.myapp.companyname.com
to allow you to host multiple...