Anything Slider on this site is quite a good slider and has a fade option. Nivo slider is also good but I had more problems in IE with it.
for Jquery plug ins an tutorials, try the jQuery website, Addy Osmani or google the particular functionality you’re after.
firebug is great for debugging – make sure you enable all the panels and reload your website once you’ve started it. Then set a breakpoint and step over each line of code to see what’s in your variables.