Which component you should upgrade first is a hard question to answer because it depends upon several factors, including your assessment of the strenghts and weaknesses of each individual component, recognition of what you are trying to change, and finally your budget.
In general, I will say that if your goal is to make the most impactful change in your system the order would go like this, from most to least: speakers, analog front end (cartridge, tonearm, phono stage/SUT, turntable), preamp, digital front end and amplifier last.
I'm not saying that the components at the end of the list do not make a difference - they do. But complete character change of a system will only occur by replacing the final transducer or the source. IMO