A new stylus certainly won't hurt, but don't go nuts. Budget should be in the $50 range, something like an Ortofon OM 5E. You may get slightly better performance with a nicer stylus than that, but if you're ready to spend $100 for a cart, you're much better off upgrading to a nicer TT. You can get some fantastic deals on older equipment that blows the doors off today's new stuff, but you have to know what you're looking at and be comfortable with tinkering.
A disc cleaning system is also a good idea, especially since you're buying used. Will help with both tracking and sound quality.