I saw Java and SQLite, but what ones are made in pure java and are platform independent? Also which would be the best to start with? I have never used sqlite but I assume it is
SQLite is getting quite a lot of hype in other language domains, however with Java you have something else available:
As for tools, well, that varies a lot. Most of the Hypersonic family products for example are mainly meant for unit testing which means that you can unit test your DB Schemas and actual queries quite easily with (almost) plain Java code.
And updated answer, you may want to try Xerial's Sqlite JDBC driver. While its current version is not pure-java, it packages binaries for major operating systems so that it is mostly portable.
Also sqlite4java also currently packages binaries for major OSes.
sqljet, which in contradiction to the name does not have SQL, but can use SQLlite databases.