Which cable is most important to spend money on...

Allocate funds for all three, because once you start upgrading, you're going to upgrade them all anyway. Determine the price level at which you can afford to purchase interconnects and speaker cable at the same time, and add power cords later...after dedicated AC lines and room treatments.

The basic idea here is to first upgrade the cable(s) that will reveal the true sonic change(s) due to subsequent upgrades (if that makes sense ;--)

So with that in mind, I'd first put a heavy duty (10 AWG wire gauge) shielded power cord on the amp and (if you have one) the power conditioner/regenerator.

Next a good quality pair of ICs between amp and preamp. Regardless of the preamp location, I believe it best to have the amp(s) close to the speakers, so speaker cable can be short -- especially with tube amps which need to be close to the speakers in order to deliver as much damping control as they can deliver. But this means the amp to preamp ICs could be long, so you want those to be the next quality acquisition.

Next, the sources. Good PCs (first) and ICs (next). Why PCs first? So you can then confidently evaluate different ICs. Some tips: PCs for DACs or CDPs should be 10 AWG, and shielded. Also, using balanced (XLR) ICs between DAC/CDP and preamp seem to give best performance, if your components allow that option.

Phono cable from tonearm to preamp (or to phono preamp) next, if you have analog. Especially important not to "cheap out" on these if you are using a MC cartridge with its inherently low output.

And last, speaker cables. Oh, they're very important, but you can evaluate all the other cable selections with comparative accuracy even using mediocre speaker cables. However, trying to evaluate speaker cables before optimising the rest of the system cabling is IMO an exercise in futility ;--)
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Source interconnect, speaker cables, power cord on source.....but first priority overall is room treatment and dedicated lines..
Larry