Which Cables Are of Most Importance?

All cable(s) are important. Your 1st replacement is the Power Cord.

Agree with Jgwilson, good quality and clean AC power is a fundamental requirement for good overall sound. Power cords do make a difference.The point is 'all' cables are important and have a sonic effect.

I recommend "source" cables first (digital cable, IC from CD player / TT) - next is speaker cables. However, you are only as good as your weakest link. My suggestion is to spend more at the source and then do speakers. Preamp to amp is next. There are so many good "budget" cables these days (Blue Jean, Morrow, and others) that you do not have to spend big bucks on cables. To me, these budget cables are so close to the big buck wires that unless you have super good ears, it will not make or break your sound quality / enjoyment. To me, it is more important to match the desired tonality (i.e copper for solid state, silver for tubes etc.....this can mitigate tonality issues like brightness or darkness in tonality). Another route is to buy "used" on this site. Thus you can try cables and not get hurt on the back end if you want to change or move up in quality.

as you see there is no agreement on which cable is the most important, there are too many variables in personal stereos to have a fair consensus for comparison.

try used cables and sell the ones you do not want and keep the ones you like

The obvious has been stated all cables matter, from my experience the preamp to amp makes the biggest difference in my system.

The least noticeable has been speaker cables.