I guess if you landed there, it’s because you already have your idea of what property graph databases are. Personally, I find the representation with nodes and links very intuitive. This, in addition to being much more flexible than relational database tables and while being more powerful in terms of analysis when you need to study relationships between entities.
Neo4j is the most popular property graph database management system. This is probably a very good option, both for learning about graphs and for production deployment.
Property graphdatabases tend to be more resource intensive than traditional SQL databases, except of course whenever you want to look for relationships between entities. Making multiple joins in SQL can be 1000 times slower.
I would like to take this opportunity to mention RedisGraph, which brings a lot of innovations in terms of performance and is very light. Coded in C++, it avoids embedding the entire Java virtual machine and also works with the Cypher query language. It uses scattered adjacent matrices to represent the graphs, with a gain in performance. For the moment the tools are not at Neo4j level but depending on your use case, it can be interesting.