Cables /power conditioner- Order of importance

Your probably getting mixed answers because it depends what your weakest link is. From what you are asking above is fair but we need to know hwat you are running now. Is your AC noisy? Are you running tubes or monoblocks or a receiver?

It all starts at the wall and I feel you should start with a non current limiting, non coloring power conditioner. The next step in the chain would be cables at the source and then work downline. The quality of the amplified signal cannot be improved once degraded.

By far power conditioning would rank first and foremost on my list. Simply because 'proper' line conditioning is so fundamental and foundational to the overall performance and listenability of a given system. It's still one of the final frontier's for many.

In fact, once you've experienced long-term listening with excellent line conditioners, you will discover that most every other system is quite fatiguing with grain, hash, negative induced siblilance, etc..

Note that I use the term 'proper' because, like any other component, there are plenty of line-conditioners that simply aren't worth much and in the case of even some very popular line conditioners the sonics are actually better when you remove the line conditioner(s) from the system.

Since my line conditioners have a built-in power cable, I consider them one and the same.

Beyond that whether the ics or scs come next might best be answered by first determining which of the current ics and scs is hindering performance the most. That would determine for me which will provide better benefit.

-IMO

If you want to upgrade many components simultaneously then consider the very top of the line Mapleshade Records power strip that does an amazing job of conditioning without resembling a traditional conditioner. It can make it seem that all your power cords have been upgraded. Just be sure that the distance between AC sockets on this or any conditioner allows room for fitting into adjacent AC sockets the physically bulky "hospital grade" plugs that may be on the ends of your power cords.
If you only need two pairs of IC's for use, first from CDP to preamp, and second from preamp to amp, then consider the lowest cost impressive IC's from Auricle Audio Design which come up for auction periodically. In a few systems, these have performed astonishingly better than their price would suggest. A truly unique handmade product from a one man shop that consistently gets overlooked in our busy Audiogon marketplace.
If you can move just a little further up the cost ladder, Reality Cables speaker wire will amaze you, once the optimized signal reaches your amplifier speaker terminals. Their IC's also compete at the highest level, still at very modest cost.
First step might be to "upgrade" all your components with the power conditioning, and then to reveal any newfound quality by insertion of quality IC's. Finally, getting it to your speakers. There is no absolute rule about which to do first, just a suggested sequence.