The first two games in legend of kyrandia have my interest, but I can't see myself playing the third game with its awful early CG backgroudns instead of the lovely hand drawn stuff from the first two. Will I be happy with just the story from 1 and 2? (no cliffhangers or frustrating loose ends to the story)

Yes, each game has a self contained story. So you won't need to play the third game. There is however a post credits scene on the second game that hints to the third one, that may be seen as a sort of cliffhanger, but you can just ignore it. In my opinion, the third game arguably ruined the story anyways and had little respect for the protagonists of the first two, the game is uglier (totally agree with you about the graphics), more silly, with a bunch of annoying characters, and adds little value to the franchise. Some people like it, though, so perhaps it's not a total waste, but it's certainly not needed to complete the story from the first two.