If you have no knowledge/experience in databases, and you are solving a problem not yet at scale, the short (but possibly unsatisfying) answer is that it doesn't matter. I would encourage you to learn more about both non-relational and relational databases to guide your thinking for specific problems.
MongoDB is the most popular non-relational according to StackShare (http://stackshare.io/databases). Perhaps you want more of a database service on top of that though, in which case Firebase is easy/cheap to get started with.
At the end of the day, each has their advantages -- for example, non-relational can give you a flexible schema and very fast retrieval -- but until you have more constraints for the problem you're solving, it'll be hard to make an educated decision.