Well you said not to suggest offal, however offal has pretty significantly different nutrients than muscle meat, and much higher concentrations of very desirable nutrients, so I think it should be part of your diet. If you don't like the taste of it so much, grind it up and include it in ground meat. Just to give an example, we bought a half steer last year and I had the guy grind up the brains (great source of omega 3) in with the ground beef, and nobody ever noticed.

I don't pay much attention to where the muscle comes from in terms of nutrition, but I do pay attention to fat content. I like Mark Sisson's idea that the fat from grain-fed animals is more likely to be high in omega 6's hence less desirable and causing more inflammation, while the fat from grass-fed and free-range animals is more likely to be high in omega 3's and help to fight inflammation. So when I am eating grain-fed beef, I find the leanest cuts I can and trim the fat, but when eating grass-fed or free-range animals, I prefer fatty cuts and eat all of the fat.