To finish my thought
Starting out get some neutral cables whether it be CAT5 or some other inexpensive option, probably just keep what you have, then go after speakers and electronics. Since the speakers are the most colored component start there, find a pair you like and build from there. The idea that you must start with the front end is incorrect. A $2000 front end driving compatible $50,000 speakers will sound waaaaaay better than a $50,000 front end driving $2,000 speakers.
If you want an immediate upgrade and want to keep the speakers, you need to go after the weak link in your system which IMHO are the old integrateds. Despite what some may think, electronics ,especially the power supplies do deteriorate and after 18+ years you are due for an upgrade.
Once you get the speakers and electronics up to a level you are happy with, then, and only then, should you consider spending more money on cables.