I agree that an outboard phono stage can result in improvement. I also agree that you'd get the most bang for your buck shopping for a used or demo unit, given your budget.
Some models I would recommend researching are the Bryston BP-2 MM, Gold Note PH-1, Simaudio 310LP (there is also the 110LP v2), Pro-Ject Phono Box RS, and Rega Fono MM.
Some models I would recommend researching are the Bryston BP-2 MM, Gold Note PH-1, Simaudio 310LP (there is also the 110LP v2), Pro-Ject Phono Box RS, and Rega Fono MM.