What's First, Interconnects or Speaker?

I think interconnects have more impact on performance than sp.cables..I would start with Digital first..At least thats what worked best for me.......

I use Transparent Audio cables. They recommend source to pre first, speaker cables second, pre to amp third.

The straight answer is do it any order you can.
Honestly I think it will depend more on the quality of the cable more than the order employed. For instance I found using Cardas Golden Ref ICs between my pre to my amps produced the biggest change for the better. Simply all around great rich tone and big sound stage with details preserved.
I would tailor your choices around the sound you want most. I used Silver Lace (pure silver) by Homegrown from my TT to phono then Millersound's clone Ultraconductor Aluminatas to pre to get the most detail from my TT. I wanted a richer fuller but detailed sound from the CD player so I used Audience Au24 from my CD player to the pre and finally Speaker cables by Jena Labs all Cu braids to my detailed speakers (Jm Labs Electra 936s).

From what I've been led to believe, you should upgrade cables from source to pre. The theory is that your system can't resolve when it doesn't receive first. If you lose it from the source, it's gone forever.

Love these chicken/egg threads.

I agree that in an absolute sense the differences in IC's will probably be more audible in a source application, but my version of which to chose first is just the opposite of many, especially if you have several sources which makes it more expensive to approach the source/IC first.

Sources sound different and you probably have several. You will want to pick your IC to match each source. They may not be the same brand/type of IC's. You will have a hard time really identifying source/IC/system synergy without already having already put together an amp/IC/Speaker (and speaker cable) which allows you to hear the differences that are made when you pick sources and IC's.

Now if you have only one source and it is the component you are building your system around perhaps starting there makes sense, but I still don't know how you will know when you have optimized its performance.