The generally accepted order of importance in an analog playback system is: turntable, arm, cartridge.
When you improve the turntable, the existing arm and cartridge will provide a higher level of performance than they previously did on the old deck. So you get an upgrade in all 3 areas at once.
When you improve the arm, the existing cartridge will perform at a higher level, thus yielding upgrade in 2 areas at once.
The cartridge improvement will yield upgrade in one area.
Of course, this is based on the assumption that the upgrade you make is truly an upgrade, and not a sideways or downward move, which sometimes happens.
So, in my opinion, doing the TT first will give the most results, even though it will likely cost the most.
When you improve the turntable, the existing arm and cartridge will provide a higher level of performance than they previously did on the old deck. So you get an upgrade in all 3 areas at once.
When you improve the arm, the existing cartridge will perform at a higher level, thus yielding upgrade in 2 areas at once.
The cartridge improvement will yield upgrade in one area.
Of course, this is based on the assumption that the upgrade you make is truly an upgrade, and not a sideways or downward move, which sometimes happens.
So, in my opinion, doing the TT first will give the most results, even though it will likely cost the most.