You might want to read about the counterweight upgrades available for the Rega RB300 arm, because it will improve all parts of the sound spectrum, including optimizing the bass.
I use Kerry Audio F2 Titanium Heavyweight Counterweight with positive effects that were quite obvious to all who heard either my Grado or Shure MM cartridges, both before and after. Unfortunately, the Grado is an old-timer no longer made, and the moderately priced Shure V15VxMR now out of production, with remaining stock moving up in price, though still below your price range.
I defer to others regarding your precise question about which MC design to provide best bass.
Please post which phono preamp you will be using since this helps determine perceived bass quality.
I use Kerry Audio F2 Titanium Heavyweight Counterweight with positive effects that were quite obvious to all who heard either my Grado or Shure MM cartridges, both before and after. Unfortunately, the Grado is an old-timer no longer made, and the moderately priced Shure V15VxMR now out of production, with remaining stock moving up in price, though still below your price range.
I defer to others regarding your precise question about which MC design to provide best bass.
Please post which phono preamp you will be using since this helps determine perceived bass quality.