The 2m black is an excellent cartridge in your budget range. It is my go to MM cartridge. For an MC cartridge, try a Dynavector 17d3 or Ortofon Cadenza. The Benz Glider is also a good performer. Each of these have good balance without being too aggressive in the treble. With the adjustment availability in the GCPH, any of them will work well. I also use a GCPH in my den system.
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Although it's *below* your budget, the AudioTechnical AT150MLX is a quick and linear performer, with nice MM body but good low level detail, with excellent frequency extension with tight bass and smooth highs. Since you're considering the Ortofon 2M Black, a similarly priced MM would be the Clearaudio Aurum Beta S MK II MKII Wood phono cartridge. Given the great reviews a closely related version received in association with the Marantz TT15 turntable.
If you go LOMC, you'll probably get more for your money from a Denon or Audio Technica in your price range, such as a Denon DL-S1 or Audio Technica OC9/III.