How high end must your system be...

Lots of factors that determine....how high end the system is is probably not a determining factor in of itself, though better systems will probably reveal more differences in general.

Try it yourself and see. You do not have to spend a lot to experiment. Start with vanilla stock RCA ICs and basic copper zip cord speaker wire from Radio Shack. Then try a few low cost alternatives that might make a difference. I'd switch ICs first before speaker wires. Try a used pair of MIT Terminator ICs. These should cost less than $50 and the difference has a good chance of being audible. If you want to go a bit higher, try DNM reson ICs, probably less than $100 used. I'm you can search other threads here on Agon and find lots of other recommendations to consider as well if you like

Speaker cables would make a difference on mid-fi systems and up, with proper equipment set-up. In my experience, more likely changing the sound signature and adding a flavor, similar to equlization. The biggest difference I've discovered though, was in power cords, primarily with tightening bass frequencies and adding (or detracting) music body weight

Don't be suckered into the 'high price better system'. Read some of the 'audio critic' stuff as putting sanity into the hobby.

While you are at Radio Shack picking up the zip cord Mapman suggested, also buy a set of their Auvio interconnects. Very nice sounding for under $20, compare favorably in my experience to wires from usual suspects that cost more.