Links to my RuneScape client installation notes on this wiki

New C++ Client

Runs Jagex Launcher and the new C++ client through Wine, surprisingly well!

RuneScape

Runs Jagex Launcher through Wine, and RuneScape native-Linux

Clients not running through Jagex Launcher only support traditional email/password RuneScape account log-ins, and 3rd-parties for RS3

Ideally you should choose the above options instead as Jagex Accounts will be required eventually and deprecate these

RuneScape (native, has interesting environment variables!)

OSRS RuneLite (Snap, Java, and AppImage)

OSRS (Java)

OSRS (Jagex Launcher + Java)

Jagex Launcher