If you're staying in Umeda / Osaka Station area, then a really good (cheap and fast) option is to take Hankyu train from Umeda straight to Kawaramachi. It's ~40min, ~400yen, goes direct without transfers (as long as you get on the right train). Going straight to Kawaramachi has advantages over going to Kyoto Sta, because Kawaramachi is in the epicenter of some of Kyoto's major highlights.