Best $500 cartridge match for Linn Akito arm

Greetings, fellow vinyl lovers. I have recently purchased a turntable rig that consists of a SOTA platter and motor installed in a custom made 45 lb. plinth. I had my Linn Akito tonearm installed on the plinth, also.

I have been reading several postings here regarding tonearm/cartridge compatibility, and I am curious of the parameters used to establish this compatibility...it seems to be the relationship between tonearm mass and cartridge weight....am I right about this?

The end point for me in learning this would be to find out which cartridges <$500 that are compatible with the Akito tonearm.

A little about me and my system: I began collecting vinyl back in the late 60's and through the 70's. Like many, I abandoned my TT when CD's were called the miracle solution to music reproduction. Over the last 5 years, I have been slowly ramping up my vinyl playback system. It now consists of:
TT mentioned above
PS Audio GCPH phono stage
BAT VK-51 SE Preamp
Spectron Musician III amp
B&W 802D speakers
Good cables all throughout.
I do enjoy reading all the various postings here, and they have served me well in educating me on how to appreciate the syenergy of making it all work together so I can enjoy the music!
Thanks in advance...