Bang for Buck

This is an impossible question to answer without testing the potential replacement components in the system. I've seen situations where a system might have an obvious weak link but it turns out the biggest change comes from replacing something completely different.

Easy, Cartridge.

Synergy is an important component, thus no generic solution can be applied to an unknown system.

Low impedance speakers may mitigate fir a better amplifier, are tubes either pre amp or amp a choice, what cartridge and tone arm are in use, etc.

One cannot determine the weak link most easily upgraded in the dark.

Loudspeakers and cartridges being electro-mechanical devices Are the most likely to make significant changes in sound quality. Chaaz just got himself a new set of speakers. Upgrading the Cartridge will have more of a positive effect on the sound than a sideways swap of integrated amps unless he was going from a pea watt amp to a very powerful one.