1 pair of good interconnects- which 2 components should I use them on?

Honestly, if a $30 pair of ICs is "much nicer" than all of your others, you should replace them all.  Your components cost several thousand dollars and you should have at least (and I do mean least) something on the level of the BJs to connect everything.  I know that's not your question, but I thought you should know. 

Haha I couldn't agree more, and when I'm out of school and not on such a tight budget I will absolutely invest in better interconnects. But for the time being (another couple of years) I'll have to live with what I've got...

My dealer always told me to upgrade your system at the "source". Get the source sounding as good as possible then move through the "chain". 

N

There is no right answer that can be predicted with any kind of certainty, as there are a great many unpredictable component, cable, system, room, and listener-dependent variables involved. And in addition, a "better" cable will not necessarily provide "better" performance in a given application, from both technical and subjective standpoints.

FWIW, though, my guess is that connecting the LC-1 between the Cary and the amp is more likely than not to result in at least slightly better high frequency extension than connecting it between the phono stage and the Cary. And the greater the length of the other cable, the greater the likelihood that will be the case. (I see that the LC-1’s are three feet long, but there was no mention of the length of the other cables).

The reason I say that is that as a tube-based product the Cary probably has significantly higher output impedance than the solid state phono stage. (I couldn’t find an output impedance spec for the phono stage; the spec for the Cary appears to be 560 ohms, at least in the Mk2 version). The interaction of high output impedance with high cable capacitance (which is proportional to the length of the cable as well as to its capacitance per unit length) can adversely affect high frequency extension, at least slightly. And the LC-1 has exceptionally low capacitance per unit length.

Of course, greater high frequency extension may not always be subjectively preferable, even if it represents greater overall accuracy of the system.

Good luck. Regards,
-- Al

Al has to be the most reasonably mannered & comprehensive contributers!