To get the official, unmodified, and "best" firmware, you should avoid random "direct download" sites. Instead, use trusted archival tools used by the XDA Developers community:

To install the Android 4.3 official firmware on your Samsung Galaxy S3 GT-I9300, follow these steps:

For the , the final official Android version released was Android 4.3 (Jelly Bean) . While newer versions like KitKat were ported by developers, they were never officially released by Samsung for this specific international model due to hardware limitations. Where to Download Official Firmware