The black goop is part of the cartridge design, it needs to stay.
Your choice of "prestige series" stylus will fit. I suppose it's just a matter of budget! Nice thing about Grado is that you can still get current manufacture, factory stylus for it. I just started playing with a Grado and haven't replaced a stylus yet myself.
I'd check the cart carefully before spending any money on a stylus unless it's known to be good. Measure resistance across each channel with a digital multimeter, each channel should read something like 500-1000 ohms and nearly the same for each channel. Then hook up the cartridge on the table gently scrape the stub of the stylus with a finger - you should get a good noise from each channel when you do that.