Wittmann is quite correct when he says that the design of destroyers (and of warships in general) varies from country to country based on each naval power’s own special philosophy and requirements. To give just three examples: American warships were in many cases intended to cope with the long distances in the Pacific, so they tended to be long-ranged (and/or to be supported by good naval oilers); British warships had to cope with the requirements of defending a global empire, but could also count on refuelling at Britain’s many possessions, so they tended to be more “short-legged” than their US counteparts; Italian warships were designed to operate in the relatively calm Mediterranean, and hence did not have to be as structurally strong as ships intended for use in the much rougher Atlantic. And even within a single country, design philosophies and practices evolved over time, based in such factors as treaty restrictions, changing operational requirements and wartime exigencies. For destroyers specifically, some designs placed a priority on a large torpedo armament, some on a powerful AAA battery, and some (like the large British Tribal class) on a large gun armament.
To answer ABW’s question, my starting point was to decide that I would pick a Japanese destroyer because this would give me a destroyer armed with the most advanced torpedo of its time, the oxygen-fueled 24-inch Type 93 Long Lance. The next step was to pick a Japanese destroyer designed after Japan broke free of the restrictions imposed by the Washington and London naval treaties, but before Japan started building simpler and cheaper designs during the last years of WWII as a result of wartime pressures.
Assuming that money was no object and that I could build as many as I wanted, my pick would therefore be the Shimakaze class. Only one was ever built, and it was considered an experimental “super destroyer” design, but it had impressive statistics: a speed of 40.9 knots (1.9 knots faster than its design speed), 15 Long Lance torpedo tubes (the only Japanese ship to have that many), and 6 five-inch dual-purpose guns (combining anti-aircraft and surface-combat capabilities). If money was a consideration, then I’d pick either the Kagero class or the Yugumo class.