Here's a site I had saved when I was getting ideas about KY Mules.
How To Make the Perfect Summer Cocktail: the Kentucky Mule
A couple of things I've found with making a good mule... or my chick has found I should say. She used to tend at Churchill Downs so she knows her chit.
1. Use Cock & Bull, Bundaberg or Fever Tree Ginger Beer. Cock & Bull is the best and they invented the drink so it doesn't get any more original. The other two are found coast to coast a bit more. My back east friends always say they can't find Cock & Bull (it's out of LA). She prefers their recipe that is on the side of the bottle except for the lime peel suggestion which is next.
2. Peel your 1/2 lime and press the bitter onto your mug, then flip it over and mix your drink on top of it. There's a lot going on in a Mule and the bitter, is as important as the sweet and spicy that the ginger beer provides and the tart the lime juice adds.
3. Watch out for recipes that call for simple syrup. Ginger beer is sweet enough. Depending on what you use, you may or may not need it. Definitely don't need it with Vodka. Cock & Bull's recipe doesn't call for it at all.
Have fun!