Neo4j DBaaS is priced based on the size of the database you choose, and you can choose a database from a single GB of RAM to 64 GB of RAM.
Pricing is quite simple at $0.09 / GB of RAM / hr with no additional fees. You're charged only for what you need and only the hours that you actually have the database. Billing stops if you destroy a database.
If you change the size of your database, you're charged for the largest capacity you use in any given hour. For example, if you start with a 2GB database at 1pm and, at 2:30pm upgrade it to 4GB, then destroy it at 4pm, you'd be charged for 1 hour of 2GB of usage and 2 hours of 4GB of usage.