You'll get more bang for the buck upgrading the turntable. Consider buying used. Try going a little higher in the Music Hall line, like a MMF-7X or 5X. I haven't heard the Classic, but it looks like a decent enough table if you prefer to buy new. It should be an incrememtal step up.
You might be able to find a decent used table with an OK cartridge at your budget and then you can upgrade the cartridge later.
If the turntable itself has issues adding a better cartridge won't make them go away. I'd rather put an inexpensive cartridge on a good turntable than a good cartridge on an inexpensive turntable. It all matters, but the turntable is the foundation.
How long have you had the cartridge?