Some people have installed mintppc on their ibook G3 clamshells and report acceptable performance. An early ibook with only 4 mb of video ram will likely struggle, even with LXDE however, and probably having more than one application open at a time is going to bog down the CPU big time.
If someone gave me that ibook (I wouldn't buy one, frankly), I'd max out the RAM, stay with Limelight (OS 9), head over to macintosh garden and have me some fun. There is tons of abandonware on that site,from Photoshop to Pagemaker and tons of 0S 9 games (not to mention virtual game station, which makes your mac a portable playstation 1). As for web browsers, icab 3.8 is horrible, but Classilla is not, and 9.3 is out this week and most web sites I go to regularly (including this one, I am typing this in Classilla) render well if not perfectly. If they don't, there is usually a mobile site that will give you the same content without all the frackin javascript and flash.
Forget about youtube or any streaming video in Limelight, it's just not going to happen. You can download and convert to mov files that quicktime will play of course, but the quality is terrible, IMHO its just not worth it.