What makes the biggest difference in sound quality?

It starts at the source and goes downstream from there. Most people here are forgetting the proper order of the signal path. If you start with garbage it only goes down from there, if you're looking for the actual information the artist intended. If you want it colored, have at it anywhere - I'm talking as neutral as possible, only worrying about distortion/noise.

1 - Source (cartridge/arm/table)

2 - Phono stage

3 - Pre amp

4 - amp

5 - speakers

If you want to put power cords and interconnects in there, place them in the order of where they touch the signal, with a power conditioner and it's power cable inserted with 1,2,3,@4 and the interconnect between the phono stage and preamp (assuming cartridge is hard wired continuously on a cable to the phono stage) between 2 & 3. Hopefully your system will allow for an integrated amp and eliminate an interconnect between the preamp and power amp.

My 2 cents.

Cabling and power cord choices choices can make a huge difference, not always in a positive manner as they are system dependent and could require experimentation.

Agree with whoever said power. After I tweeked everything else added EquiTech 2RQ. Was blown away. Made a bigger difference than about every other change combined. Don't care how top end your setup is, if you are feeding it noisy AC, your gear is operating with one arm tied behind it's back.

Of the choices provided, my experience is that interconnects and speaker cables first, power cabling, and then fuses. I believe the answer is relative to the quality/performance of the item getting replaced.  For example, going from 14 gauge Kimber cable speaker wire to Transparent Reference XL speaker cables was a dramatic change for me. Subsequent change unlikely to be that dramatic.

Similar to other posts, I believe there are things that take priority over the items mentioned. 

Electric signal.  I installed a separate meter connection for my electric, direct wired to audio room, with 6' deep copper pipe grounding and separate panel. If the electrical signal is nasty to start with, nothing (IMHO) can fix that. SQ will suffer.

Room treatment. Bottom line.  If properly analyzed & installed, acoustic treatment  will make any system sound significantly better, if not great.

I don't believe using a full loom of cables from just one manufacturer makes sense regardless of the fact that we have one such punting his product here. Is this self promotion actually allowed?

The idea is put forward as staying with a certain house sound. When designing for instance a speaker cable, the purity of wire, the metallurgy of the connectors, the dielectric properties of the insulation and decorative outer covering all impact on the result. Now look at a USB cable, with different power requirements and vastly different types of connectors. How does the designer create his cables to adhere to his idea of the ideal 'house sound' ?

After sorting out the room which is paramount one can then try different cables, fuses, amps etc. Without taming the room by reducing the overly long time the sound takes to decay which is adding smear and obscuring detail, any  attempt at improving the system is doomed. For example, sound way too bright...add tubes and on and on.

You will never hear any manufacturer telling you to: "get back to me after you've treated your room" What you get is: "Buy a full loom of our cables to sort out all your problems.

Happy new year to all 🍺 🍹