Bang for Buck

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.

If you are searching for a global/generic recommendation, then always choose transducers first. The cost to benefit ratio applies more reliably with mechanical/electro-mechanical devices over pure electronics.
It all matters, of course, but bigger chunks should be spent on mechanical devices.
Ahhh...mijostyn beat me to it while I was typing!

Did two threads get merged here?  I seem to remember several of these posts on a completely different thread (including mine).