Disclaimer: I work for/with Neo4j
Just talking about the maturity here (not technicalities) – Neo Technology as a company with more than 50 employees, $25M funding and a thriving user-base with half a million downloads, 30k new databases running each month and an active community won’t go away. You can also check the SO questions to see the community activity.
We have a healthy set of customers in many domains from big ones like Adobe (runs creative cloud on Neo4j), Cisco (Org-Management, MDM), social networks like Viadeo and many Job search companies (GlassDoor, and others) to startups like fiftythree who published the popular “Paper” app on iOS.
Our community site neo4j.org should be a good place to go, to get started, you find there introductory content as well as information on programming languages, drivers and deployments that should help you get started.
Emil, Ian and Jim wrote an introductory book about “graph databases” with O’Reilly which is currently available as a free ebook download.
So you see we’re not just taking care about our own product but also the bigger graph ecosystem, also with many conference talks, meetup groups (41 worldwide) and support of the open source ecosystem.
Hope that helps you deciding.
P.S. Regarding your concerns:
The size limits (which are artificially anyway) will be increased this year.