Champagne Cocktail

This is the modern Champagne Cocktail as prepared for most of the 20th Century (and the 21st...).  The admonition to avoid stirring is present in the instructions for a reason. 

This current method of constructing a Champagne Cocktail produces a drier drink because the sugar does not have a chance to fully dissolve.  Soaking with the bitters will dissolve some of the sugar, and immersion in the Champagne with it's bubbles will get it further along.  But when you finish the drink you will probably still have some undissolved sugar left in the glass.  This is intended and produces a slightly sweeter flavor profile than the Champagne by itself.

If you desire more sweetness give the drink a quick stir before garnishing.  Be careful not to stir too much or the Champagne will spend it's bubbles and your cocktail will go flat.

I also like to use other types of bitters in this drink.  One fine choice is Bitter Truth Old Time Aromatic Bitters which seem to be a little more delicate than Angostura.  This pairs nicely with a delicate Champagne.  

As to what kind of wine to use, use a good sparkler.  A Champagne Cocktail is 90% or more wine so use a quality California sparkling wine or a non-vintage French Champagne.  You don't need to go nuts with a vintage Champagne - you would just be covering it up with the bitters and sugar.

Substitute absinthe for the bitters and top with a 1/2 oz of good Cognac and you have a Casino Cocktail. Or stick with the bitters and keep the Cognac float (David Wondrich advises trying Peychaud's bitters if you are adding brandy).

Champagne Cocktails started out in the mid-19th Century as iced drinks.  This evolved over the years to using less ice and finally to the version we have today.  If you want to use some ice go ahead and add a large cube or lump of ice before garnishing.  This can extend the drink a little during warm weather.