I'm new to the world of red meat also, having been a vegetarian for years and then only eating fish and poultry for many years after that. I started eating grass-fed beef after reading "The Omnivore's Dilemma". I used to wish there was a cookbook entitled "The Vegetarian's Guide to Meat" because we were so clueless!
Here's what my husband and I have been successful with: burgers (of course), beef stew, kabobs with beef or lamb, lamb chops, braised lamb shanks, flank steak (on the grill), and pot roast. Pretty basic stuff. I'm scared to buy a good grass-fed steak at $17 a pound and then ruin it. I love chicken thighs and whole roast chicken. We bought some ground pork and made Skinless Gyozas from a recipe video here at MDA, which were great! We are also heavy eaters of bacon and sausage. Luckily we can buy all this meat directly from local farmers.