A new cartridge on dirty records is not worth the investment. So you must have a record cleaning solution. Even a SpinClean or a DIY US device. Assuming that's in order, and your turntable, tonearm, and phono amp are up to the job, a cartridge will bring a significant improvement. However, a poor phono amp won't even allow your existing cartridge to shine. Neither will a poor support structure under the turntable. Or dirty power. See where were going here? It's all interdependent, and without more information on your system, you're not going to get the best value answer.
Phono Stage, Cartridge, DeGritter...which one first?
If you were considering any of these changes, which one would make the most immediate improvement without narrowing it down to a specific phono stage or cartridge...interested in some feedback from the analog folks here.