You need at least Java 1.7 to run tinyMediaManager. You can get Java from https://www.java.com/ (Linux users can download Java from the package repository of their distribution too).
The release build is recommended for all users.
Pre-Release builds are built a few days before we publish a new release. This build is rather stable but still can contain some bugs. This should be used for testing purposes.
Nightly builds are automatically built every day and should only be used for hunting down bugs on test files. These build may contain severe bugs which can delete/destroy your test files!