Geetams are among the first compositions we learn as Carnatic Classical students. Malahari, Suddha Saveri, Kalyani and Mohanam are introduced among other ragas, at the geetam stage.
Since it is something most of us learn in the beginning, it makes sense to start with the Geethams when learning to connect Indian classical with Western harmony.
The Geetams can be broadly divided to Mayamalavagowla based and Major scale (Shankarabharanam) based. Understand why a particular set of chords are used for the melody, and you can use similar or same principles to find chords for any raga, melody, phrase or song.