Just wanted to check, if I want to listen to my clip zip through my stereo, do I buy a 3.5mm to 3.5mm connector? Like this one?: http://www.newegg.com/Product/Product.aspx?Item=N82E16826787004&name=All-Headphones-Accessories
Depends on what type and size of AUX IN or input jack you have on your computer. If it’s 3.5mm (1.8") then yes, what you linked to should work. Double-check though, RCA -style plugs are much more common on stereo equipment than 3.5mm jacks are.
Also don’t use the phono input on your stereo. Any other input(besides a mic input) will be line level and will work fine.