Bang for Buck

Limited budget upgradeWill I get more bang for buck with a Integrated Amp upgrade or a Phono Stage and Cartridge upgrade?Buying new speakers and have some budget left over. This is a single source, Phono only, system.
What are the components of the current system?  Without that knowledge, it's completely impossible to say which element would be the "weakest link" and would be the first to upgrade.
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.

I just repaired an old Counterpoint SA-3000 which includes a phono section.  It is NOT an integrated unit just a preamp.  The phono was quite good having a really nice, sweet mid-range, So that may be an option plus they are not that expensive and can be upgraded for cheap.

Happy Listening. 

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.