Sue, I think any and all cuts are fine. I think grass-fed is far superior health-wise and one important step above organic. I hope you have access to a farm-supplier. There are also farms around the country that ship meat which might bring down the price if you have a place to store it. Do you live near a Whole Foods?They sell grass fed beef.
I too only ate red meat 1x per week, and this was the first thing Dr. B told me to change. It has really helped me on this diet. I make meatloaf "muffins" with an egg and some yeast-free bread crumbs and garlic powder and salt. When I started list two, I added sauteed onions to my meatloaf muffins. These are great to freeze. Over the holidays my sister made some turkey gravey with the water from boiled tukey innards, some celery/carrots and a few mediterranean herbs. We added butter and spelt flour and had a nice gravy to freeze and serve with the meatloaf. You also can make the olive oil mayo with garlic powder/salt and spread on hamburgers or meatloaf. Sometimes we splurge and make a ribeye or other cut. When you can add in tomatoes you can make a beef stew. I haven't done that yet. On list 3 I make a beef and bean "chili" with mild paprika and oregano if tolerated. I serve it with yogurt, avocado, cheese. Dr. B ok'd for list 2/3 Alvarado Street Sprouted Wheat tortillas which I eat with the chili. No yeast, bad oils, or sugar or other weird stuff. Hard to find. Some people make their own tortillas. 
I was also glad I checked with my local butcher because they make some beef and chicken sausages without sugar, wine or yeast, and with herbs I can tolerate. It is worth asking around. They have been a nice addition!!