Cognac is always sipped neat. Get a snifter and cup it in your palm. The heat from your hand is enough to open it up.
Brandy is distilled wine. Cognac is brandy from the Cognac region of France, and Armagnac is brandy from the Armagnac region of France. Armagnac has some apple flavor, and I love it.
Good entry-level Cognac is VS (or very special) Hennessy or Courvoissier. Next step up is VSOP, or very superior old pale. Top of the heap is XO, or extra old. The designations are about the length of storage before bottling.
Remy Martin and Martell are also quite good. You have to taste your way through these in order to gauge your tastes.
I'll take a good Cognac or Armagnac over a good bourbon or scotch any day.