A few options from someone who has been down your road recently. Not sure I would say any of these is the "right" way to go, but any of them will make an audible difference.
One, I don't have any experience with your receiver, but if you're thinking about upgrading your amp the NAD C316BEE is a great option. It brings that classic NAD class AB sound, and has a really good MM phono stage.
Two, I'll echo the previous post about upgrading your phono cart. A big improvement can be had by upgrading/updating to one of the Sumiko oyster carts, the Nagaoka MP series, or the AT VM that was previously named.
And third, if vinyl is your primary media, think about a record cleaner. I use the Record Doctor, which made a big difference in audible quality of my vinyl for not a huge investment. And if you play a lot of used vinyl, an inexpensive ultrasonic cleaner makes a remarkable difference.
Good luck and enjoy the music!