Hard shifting, manual transmission. on 2002 Pontiac Sunfire

Moving the shifter forth and back is easy, but de right-left movement is hard, ans the shifter does not center itself. I also have a hard time engaging first gear. I tried to lubricate the corresponding transmission cable at the transmission end, but didn't change anything. Is the cable faulty or is there a problem in the transmission.

Thank you very much for insights.

Could be a worn binding shift cable or shift fork inside tansmission is binding. If it has a console around shifter that needs to be removed to inspect shifter cables.