I like actual medium (hot pink center) steaks which means I order medium rare. But I find my tastes are veering a little rarer as time goes one. NY Strips are definitely my favorite cut, though a good prime rib is always awesome.
For obscure meats, bison is awesome: I highly recommend anybody try it when they get the chance. Ted's Montana Grill is a small restaurant chain that serves bison steaks and burgers that are really good. I also liked gator when I tried it. And I'll eat pretty much any kind of game bird but that's probably a bit too far off-topic.