I went through a similar exercise this summer. Maybe my experience can be helpful. I have 15 year old Mountain bike with XTR components all around. My 6 year old chain starting to bind in a couple of links so I decided to change it out. I did not buy a Shimano chain but used a KMC 8 speed chain from LBS. I made the mistake of throwing out the old chain. I could have soaked it in degreaser and fixed it. I started skipping immediately, I decided since both the cassette (XTR) and front cranks/rings (XTR) where at 10 years old I might as well change them out. I ordered a new shimano 8 speed cassette and new shimano cranks, plus a new bottom bracket. Since shimano does not make any high end 8 speed stuff I had to settle for what they had. I was not in the mood to purchase used XTR that matched.
(I am not by any means a pro rider and I live where mountain biking offers few challenging places to go, so I don't need XTR, I have become a component snob unfortunately.)
The cassette came in right away. The cranks were back ordered. So I changed out the cassette and it still skipped. I couldn't figure it out until I realized that the front chain rings were skipping. It was imperceptible, even looking at the front chain ring while riding I could not see the chain skipping but I could feel it skipping. So I was nervous when the cranks came in. I installed them, re-tuned everything again. Viola, the bike was back to perfection again. I have ridden about 250 miles on the toughest terrain that Chicago land has to offer and no skipping what so ever. And amazingly enough, now that I have some lower end components I can still ride. The lower end stuff I installed has made no discernable difference in my experience.
So see if your front rings are worn out. If so, change the rings if you can or change the entire unit. Generally you should change the chain depending on riding, about every 500 to 1000 miles. Change the cassette a bit less frequently and change the rings a bit after that. If you use a worn chain it will grind and wear out the cassette and chain rings prematurely.