Is there a way to filter option where ONLY
system.debug statements are listed and nothing else?
you can go to debug logs and click on 'filter' beside your user under monitored users.
apex debug codes are usually placed under the 'debug' level so set the other levels to 'none' and adjust accordingly :)
You can open the developer console, run whatever transaction you are debugging, open the appropriate log, and select the Debug Only checkbox in the bottom left.