Transportation from Kansai International Airport (KIX, Osaka) to Kyoto Station
The most comfortable option is Japan Rail (JR)’s limited express ‘Haruka’. The Haruka will take you to Kyoto Station directly. It takes about 75min. There are two railway companies operating, JR and Nankai. JR is best for southern Kyoto where your house is.
Even if you don’t hold the Japan Rail Pass the Haruka can still be a cheap option. Overseas Tourists can buy a 1 day JR West Kansai pass. It is only 2,200 yen with the early bird discount and gives you unlimited access on the Haruka plus all other JR trains within the Airport, Nara, Kyoto and Himeji (except bullet trains). The one way fare on the Haruka from KIX to Kyoto is 3,170 yen (unreserved seat ticket), so you save money even just going to Kyoto. You don’t have to pre-purchase the JR West Kansai pass before you arrive in Japan, you can get it from the ticket office at JR Kansai Airport Railway Station, and it only takes five minutes once you show your passport.
At Kansai Airport Station the Haruka departs from platform 4.
JR West website: https://www.westjr.co.jp/global/en/travel/shopping/access/train.html
Japan Travel website: https://en.japantravel.com/kyoto/best-way-to-and-from-kansai-airport-to-kyoto/404
By highway bus:
You can take high way bus to Kyoto from Kansai International airport as well. Here is the website for the highway bus system. This bus will take you to Kyoto station Hachijo-exsit (south side).