The Old Fashioned owes its birth to heavy, harsh whisky, of the sort less seen today, and the need to ameliorate the "bite". Brands like Old Crow or Old Forester have the harsher "edge" befitting the cocktail, and other than Jim Beam's Rye or Old Overholt, there are just not many of the old style "heavy" ryes around. Don't bother with expensive Bourbon or Tennessees, especially sour mashes, as they are lost in the drink.

The classic, a thin slice of lemon, a teaspoon of castor or granulated sugar and a good multi-dash of bitters in the bottom of a heavy short glass, then "muddled" together with a sturdy cocktail spoon, adding an ounce of water (@room temp) stirred to dissolve sugar, then big, cold ice cubes (to slow melting), and about 2+ ounces of whisk(e)y as described above to fill the glass. I prefer the result "unstirred" to give slightly different flavors as consumed. The result and the tradition is a "strong drink", not an insipid watery mess.

The classic garnish involves a 1/4" slice of orange hooked over the glasses edge anda stemmed maraschino cherry. An old style bartender will leave the muddled lemon in the bottom to demonstrate the provenance.

.....But then, I prefer a Manhattan "Up", and made with Canadian whisky, sweet vermouth and a drop or two (less than a "dash") of bitters, and consider Persian limes as little more than colorful additions to a fruit centerpiece (Cocktail recipes benefit from ripe, light green Key limes), Martinis served in unchilled glasses are an affront to public decency, and a good host must have a flourishing mint bed beneath condensate drain of his HVAC as a well as silver goblets or stirrup cups, if he intends to offer Mint Juleps (and mint muddles best with heavy simple syrup, not granulated sugar).
"Sterling Silver" (Status conscious guests, especially FT-types, always look for proff marks.) and Dickel's #12 elevate the drink above celebrity swill class.