saving as PNG in PS7

I usually save all my icons as jpgs, but lately people have been telling me png is a better way to go. I didn't even notice that there was an option for png at first under "save as web" (which is what I use all the time) but I don't know what the difference is between "PNG-24" and "PNG-8 128 Dither." I'm trying to get the best quality possible while still having a decent filesize, so will someone tell me which would be the better to use? Thanks!