Which is more important in transmitting the sound, the information...

Not sure why this question is causing so much confusion. The OP is asking whether he/she should first upgrade the CD to pre-amp or the pre-amp to amp IC.

And I'll avoid the short answer (which is that interconnects don't make much difference) because there's a LONG meandering thread on that already.

MC - great answer!

Maybe the OP didn't use the correct terminology, but I'll provide an answer to his query. Throw out the part about shaping the sound, it's vague and shouldn't apply. An equalizer and tweaks shape the sound.

IME, the interconnects from CDP to preamp will have the greatest impact and influence on the sound. Start at the source. You want a cable that will faithfully transfer the signal (information) to the preamp.

 

You can easily solve the problem by buying two new cables and inserting one on the CD player and one from amp to preamp.