It all depends on what you need. There is no "use this DB for huge applications". Definitely don't use SQLite in production as it doesn't scale.
MySQL - can scale well if used correctly and was used by Twitter for a long time
PostgreSQL - is currently on the rise and a lot of gems start to support it aswell.
MongoDB - is a NoSQL database and can come in very handy when you have a lot of documents to store. It scales very well as you can just add new nodes on the fly.
Oracle - I don't have any experience with that one.
As you can see it is not possible to answer your question just based on "which DB is faster and (whoch one) can maintain a big DB". You have to be more specific on what kind of data you want to store. Do you have highly connected data? Then you might want to take a look at a graph database like Neo4j. Do you have a lot of unstructured data with varying attributes? Take a look at MongoDB.