Running GUI application from Console Login
Safari won't run under Xquartz/X11 which themselves need a non-console session to run.

You could select a web browser that runs under X11 exclusively and boot to a unix OS other than OS X and accomplish your needs.

Alternatively, you could set up a managed user on the Mac and have it launch Safari. Depending on what you need, parental controls or simple finder and dock hiding might be able to accomplish your goals - but the kiosk software is sold since they've engineered a solution where the OS doesn't have a setting to simply enable equivalent functionality.