First off, your mint julep should not be the size of a supertanker or a thirsty-two ouncer. It should be the size of a julep cup (10 oz., 12 max.). The idea is something that will not heat up too much. Like so many drinks, it must stay cold while you're drinking it. That's the top consideration.
It should not be unduly sweet unless you are a southerner. If you're a southerner, feel free to make it as sweet as you like, and even use Southern Comfort, as they do at the Derby (though I'm obliged to say that though the Derby is storied, the julep has been around for even longer---if anything, and the Derby only adopted the julep as a preferred drink in 1938). But if you are from anywhere north of Mason County Pennsylvania, you'd better watch the sugar.
The silver cup is an affectation if it doesn't have a rim at the bottom. There's a rim at the bottom so you don't warm the cup with your hand. A rimless julep cup is an affectation.
Here's the best recipe anywhere---again from Doc's CocktailDB
Fill with shaved ice
Stir until frosted
Ah, 2 oz. bourbon in a mint julep. Yes. That's so you bet the right horse.
If you'd like more info and some good links on the mint julep, check Colleen, she's sort of the mint julep clearing house. The largely historical article at wikipedia is of considerable interest.
And what bourbon whiskey?
For me, dear old Jim Beam works best. For you?