Summarize:

Instead of ordering a replacement stylus, look online to find compatible styluses for your turntable. There are 4 main stylus models, and each has their own benefits and drawbacks. Check a stylus manufacturer's website to find out if a new stylus will fit on your brand of turntable. Keep in mind, unless you have a great ear, you may not recognize much of a difference between your stock stylus and the new needle.
Order a different type of stylus if you want to upgrade your sound.