Yes, it can be quite difficult to find the right bread for a burger. It shouldn't take away from the texture of the meat itself, but should be solid enough to hold it (and whatever else you want to put in there).
I have a particular hatred of generic, foamy bread. Sourdough works pretty well, I think, as long as it's not the more chewy varieties. My personal favourite, however, is a Scottish morning roll - the kind with the rice flour crust on top. Naturally, they suit a square sausage best of all, but they do a good job with a burger.
Also... It's not just about the quality of the mince, but the type as well. IMHO steak mince isn't the right type to use - a slightly fattier cut (or at least some of the fattier cut mixed in) does wonders for the flavour.