It depends. Since husband doesn't eat red meat, burgers made at home are always turkey burgers, so they're well done. Not dry cooked-to-death, but cooked through. When dining out, I usually have a beef or bison burger, in which case I order them "medium".
As for toppings, my favorite is crumbled blue cheese or blue cheese dressing, along with ketchup, dill pickle relish, sliced fresh tomato, & sliced raw sweet white or red onion.
However, to be honest, I've never met a burger I didn't like, & also enjoy them with everything from a mundane slice of melted American or Velveeta, to cheddar, swiss, mushrooms, etc. The only thing I've never warmed up to on burgers is bacon. Somehow I just find the salt & smokiness too overwhelming.