Good quality minced beef usually chuck with a bit of rump, a 1/4 lb burger press then chill for a while to firm up, good old S&P before cooking. I prefer my burgers on a flat top cast iron grill cooked to medium rare (IF I mince it myself or get it from my butchers). As to buns, totally non traditional, we've used wraps folded to a triangle with burger in one side and salad or "bits" in the other fold. Recently we've taken to using sandwich thins on flavoured burger if there is a substantial BBQ to be eaten. There was an interested forum debate on which was more important for taste, the burger or the addornments.
As to flavoured burgers, sweet sauteed onions, minced garlic or roasted garlic work well, finely diced cheese (if cooking to medium) added will keep the burger moist. There was an excellent link (which I can't find) where experiments were conducted into adding salt to your mix before cooking which apparantly took away all of the texture turning it into a mush.
Oh and although it wasn't called a burger, at the Colesium in good old ancient Rome you could buy, along with your cornucopia of dried fruits, a cooked, flattened meat ball between slices of bread, doused (sadly) in Garum (think Thai fish sauce on steroids)
