What free service can be used for data warehouse with REST backend?

Question

RESTful API

Hello. I want to make an extension for Google Chrome. To store and synchronize data, you need a backend with a database. It is necessary to implement a REST service with CORS support, which can also be used for mobile versions of the software.
I had no experience with tools such as heroku and mongolabs, I wanted to ask people who deal with these platforms if it is possible to organize something similar on them (using a free plan) and what pitfalls there might be. Thanks in advance.