Going from 3 to 2 chainrings should be fine and not require a new derailleur or shifter. Note that double-chainring cranksets usually require a narrower bottom bracket than triples do.
Rear road hubs are either Shimano or Campagnolo-compatible. Many brands are available in both versions.
Degreaser and a stiff-bristled plastic brush work well on cassettes.
Wheels are rotating weight, so upgrading them will likely make the biggest difference. After them, I'd upgrade the forks.