What kind of database? An embedded key/value database like TokyoCabinet? An embedded SQL database like SQLite? An in memory data-structure database like Redis? A server SQL database like MySQL? A distributed key/value database like Cassandra? A json document database like CouchDB? I could go on...

In general, if you want to learn a new language, pick a project of limited scope (weeks) that you have done in the past in some other language.

A database is a bad choice. Even the simplest database worth being called a database requires months of effort.