Upvote:4
If by Minami you mean the Southern area of Osaka, in the sense described by Japan Guide, you're probably looking to go to Namba.
From Kansai you have a few options, you can take the Nankai-Kuko line, the Nankai Limited Express or JR Kansai Rapid Service. These will cost you anywhere between Β₯920 to Β₯1400, unless you have the JR pass which makes the trip free (except for the subway, if you decide to take that in the city)