yes, the composite cables will be all you need to get the best picture. The difference is definitely noticeable. Mostly it is sharper and the colours more vivid.
After you buy the cables:
go into the Wii Options from the Main Menu
Choose Wii Settings
Choose EDTV/HDTV (this button will not be selectable unless component cable is plugged in)
also be sure you have set up widescreen in the options too, if you haven't already.