Most important vinyl component to upgrade first ?

Well, generally speaking, the most important component to upgrade first would be your weakest one.

I take a very different tack, that of a music lover, not an audiophile, and that is to upgrade your collection of software before anything else.

That said, the cartridge/tonearm interface is really an area of black magic and it is worth doing whatever is possible to find a sympathetic combination. If the best arm and the best cartridge won't play nicely together the result will be utter crap. Throw as much money as you want at the problem and it will not help.

All things being equal, and although the distortions that they generate are a magnatude less than the distortions in transducers, I find that electronic distortions are the most jarring to the ear and most destructive to the fabric of the music. So, if the system was competely balanced, the tonearm/cartridge interface maximized, I would look to the phono preamp.

Happy listening.

The most critical unit in analog reproduction is the Phono Stage. There is absolutely no way to degrade a signal more than here [Only exception: Using MM Cartridge, then it is not necessary to think about a high quality Phonostage].
Your 1-5 list is correct.

The cartrideg I find makes a really big difference. That said a crappy phono stage will ruin anything the cartridge is sending it.