Quadphile,
Any good cartridge/stylus will work for SQ. The only "finicky" cartridges are those designed for CD-4, as they have to be able to pick up the supersonic signals that CD-4 use to encode 4 channel information into 2 stereo channels.
Be sure your cables are in good shape, not that you need $400.00 cables, just good audio cables that you can get for around $15.00 or so, and yes, it is worth the expense.
As for the turntable, I had the same problem with a shure turntable and solved it by getting some 90% alcohol to remove the old belt residue and you should be able to google a replacement belt.
Give all the audio pots and switches a dose of De-Oxit and then try out the system. I think you will like what you hear.
MTGC (Michael)